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LECTURES ON 



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LECTURES 



LOGIC 



SIE WILLIAM HAMILTON, BAET. 






EDITED BY THE 

REV. H. L. MANSEL, B.D., LL.D. 

AVNpr.nTE PR0KR59OR OK MORAT, AND MRTAPIIVSICAI, nill.OSnFUV, OXKOP 

AND 

JOHN VEITCH, M.A. 

PROFESSOR OF LOGIC AND RUKTOniC IN THK UNIVEBSITV OP GLASOOW 



VOL. II. 

SECOND EDITION, EEVISED 



WILLIAM BLACKWOOD AND SONS 



s^ EDINBUEGH AND LONDON 

^s^v MDCCCLXVI 



The PJf/ht of Translation is referred 



CONTENTS OF VOL. 11. 



LECTUEE XXIV. 
PURE LOGIC. 



Page 



PART II. METHODOLOGY. — SECTION I. METHOD IN GENERAL. 
— SECTION II. METHOD IN SPECIAL, OR LOGICAL ME- 
THODOLOGY.— I. DOCTRINE OF DEFINITION, . . 1 

LECTUEE XXV. 

METHODOLOGY. 

LOGICAL METHODOLOGY. — II. DOCTRINE OF DIVISION, . 22 

LECTUEE XXVL 
LOGICAL METHODOLOGY. — III. DOCTRINE OF PROBATION, . 37 

LECTUEE XXVIL 

MODIFIED LOGIC. 

PART I. MODIFIED STOICHEIOLOGY. — SECTION I. DOCTRINE 
OF TRUTH AND ERROR. — TRUTH — ITS CHARACTER AND 
KINDS, 60 

LECTUEE XXVIIL 

MODIFIED STOICHEIOLOGY. 

SECTION I. DOCTRINE OF TRUTH AND ERROR. — SECTION II. 
ERROR — ITS CAUSES AND REMEDIES. — A. GENERAL 
CIRCUMSTANCES— SOCIETY, 75 



viii CONTENTS. 



LECTURE XXIX. 



Paoe 



ERROR— ITS CAUSES AND REMEDIES.— A. GENERAL CIRCUM- 
STANCES — SOCIETY. — B. AS IN POWERS OF COGNITION, 
FEELING, AND DESIRE. — L AFFECTIONS — PRECIPITANCY 
— SLOTH — HOPE AND FEAR — SELF-LOVE, ... 89 



LECTURE XXX. 

ERROR — ITS CAUSES AND REMEDIES. — B. AS IN THE COG- 
NITIONS, FEELINGS, AND DESIRES. — II. WEAKNESS AND 
DISPROPORTIONED STRENGTH OF THE FACULTIES OF 
KNOWLEDGE, 109 



LECTURE XXXL 

ERROR — ITS CAUSES AND REMEDIES. — C. LANGUAGE. — D. 

OBJECTS OF KNOWLEDGE, 140 



LECTURE XXXIL 
MODIFIED METHODOLOGY. 

SECTION I. OF THE ACQUISITION AND PERFECTING OF KNOW- 
LEDGE. — I. EXPERIENCE. — A. PERSONAL : — OBSERVATION 
— INDUCTION AND ANALOGY, 152 

LECTURE XXXIIL 

OF THE ACQUISITION AND PERFECTING OF KNOWLEDGE. — 
I. EXPERIENCE.— B. FOREIGN: — ORAL TESTIMONY — ITS 
CREDIBILITY, 175 



LECTURE XXXIV. 

OF THE ACQUISITION AND PERFECTING OF KNOWLEDGE. — 
I. EXPERIENCE. — B, FOREIGN : RECORDED TESTIMONY 
AND WRITINGS IN GENERAL. — 11. SPECULATION, . . 191 



CONTENTS. IX 



LECTURE XXXV. 



Page 



OF THE ACQUISITION AND PEKFECTING OF KNOWLEDGE. — 
III. COMMUNICATION OF KNOWLEDGE. — A. INSTKUCTION 
— 0£AL AND WKITTEN. — B. CONFERENCE — DIALOGUE 
AND DISPUTATION, 204 

APPENDIX. 

I. — THE CHARACTER AND COMPREHENSION OF LOGIC — A 

FRAGMENT, 229 

II. — GENUS OF LOGIC, 233 

III. — DIVISIONS, VARIETIES, AND CONTENTS OF LOGIC, . 239 

IV. — NOTE OF LOGICAL TREATISES RECOMMENDED BY SIR 

WILLIAM HAMILTON TO HIS CLASS, .... 244 

V. — LAWS OF THOUGHT, 246 

VI. — NEW ANALYTIC OF LOGICAL FORMS — GENERAL RE- 
SULTS — FRAGMENTS. 

{a) EXTRACT FROM PROSPECTUS OF ' ' ESSAY TOWARDS A NEW 

ANALYTIC OF LOGICAL FORMS," .... 251 

(b) LOGIC, — ITS POSTULATES, . . . . .254 

(c) QUANTIFICATION OF PREDICATE,— IMMEDIATE INFERENCE, 

— CONVERSION, — OPPOSITION, .... 257 

(d) APPLICATION OF DOCTRINE OF QUANTIFIED PREDICATE TO 

PROPOSITIONS, ...... 279 

(c) APPLICATION OF DOCTRINE OF QUANTIFIED PREDICATE TO 

SYLLOGISMS, ...... 290 

(/) OBJECTIONS TO THE DOCTRINE OF A QUANTIFIED PREDI-, 

CATE CONSIDERED, ..... 296 

ig) HISTORICAL NOTICES OF DOCTRINE OF QUANTIFIED PRE- 
DICATE, ....... 305 

VII. — CANONS OF SYLLOGISM ; GENERAL HISTORICAL NO- 
TICES AND CRITICISM. 
A. HISTORICAL NOTICES. 

(a) FUNDAMENTAL LAWS OF SYLLOGISM — QUOTATIONS, . 324 

(b) FUNDAMENTAL LAWS OF SYLLOGISM — REFERENCES, . 346 

(c) ENUNCIATIONS OF THE HIGHER LAWS OF SYLLOGISM, . 348 



X CONTENTS. 

VII. — CANONS OF SYLLOGISM — continued. 

Page 

{d) OBJECTIONS TO THE DICTUM DE OMNI ET NULLO, . 350 

(c) GENERAL LAWS OF SYLLOGISM IN VERSE, . . . 350 

(/) SPECIAL LAWS OF SYLLOGISM IN VERSE, . . . 351 

B. CRITICISM. 

(a) CRITICISM OF THE SPECIAL LAWS OF SYLLOGISM, . 352 

{b) LAWS OF SECOND FIGURE, ..... 355 

(c) author's supreme CANONS OF CATEGORICAL SYLLOGISMS, 357 

(d) ULTRA-TOTAL QUANTIFICATION OF MIDDLE TERM, . 358 

VIII. — INDUCTION AND EXAMPLE. 

(a) QUOTATIONS FROM AUTHORS, .... 365 

(S) MATERIAL INDUCTION, ..... 375 

IX. — HYPOTHETICAL AND DISJUNCTIVE REASONING — IM- 
MEDIATE INFERENCE. 

A. author's DOCTRINE— FRAGMENTS, .... 376 

B. HISTORICAL NOTICES, ..... 395 

X.— SORITES, 403 

XI. — SYLLOGISM. 

A. ITS ENOUNCEMENT — ANALYTIC AND SYNTHETIC— ORDER OF 

PREMISES. 

(a) ENOUNCEMENT OF SYLLOGISM, . . . 406 

(b) ORDER OF PREMISES, .... 409 

B. FIGURE — UNFIGURED AND FIGURED SYLLOGISM. 

(a) CONTRAST AND COMPARISON OF THE VARIOUS KINDS 
OF FORMAL SYLLOGISM — DIFFERENCE OF FIGURE 
ACCIDENTAL, ...... 412 

{b) DOUBLE CONCLUSION IN SECOND AND THIRD FIGURES, 414 

C. HISTORICAL NOTICES REGARDING FIGURE OF SYLLOGISM, . 421 

D. SYLLOGISTIC MOODS. 

(a) DIRECT AND INDIRECT MOODS, . . . 458 

(b) INDIRECT MOODS OF SECOND AND THIRD FIGURES, 464 

(c) NEW MOODS — NOTES UPON TABLE OF SYLLOGISMS, . 466 

XII. — LOGICAL NOTATION. 

(a) LAMBERT'S LINEAR NOTATION, . . . 469 

(b) NOTATION BY MAASS, .... 472 

(c) author's scheme of NOTATION — NO. I. LINEAR, . 473 
{d) author's scheme of notation— UNFIGURED AND 

FIGURED SYLLOGISM — NO. II., . . . 477 

(f) author's scheme of notation — FIGURED SYLLO- 
GISM — TABLE OF MOODS — NO. III., . . 485 



LECTURES ON LOGIC. 



LECTURE XXIV. 

PURE LOGIC. 

PART II. METHODOLOGY. 

SECTION I. METHOD IN GENERAL. 

SECTION II. METHOD IN SPECIAL, OR LOGICAL 

METHODOLOGY. 

I. DOCTRINE OF DEFINITION. 

Gentlemen, — We concluded, in our last Lecture, the lect. 

XXIV. 

consideration of Syllogisms, viewed as Incorrect or '- 

False ; in other words, the doctrine of Fallacies, in so JJ^'j!*"^' 
far as the fallacy lies within a single syllogism. This, 
however, you will notice, does not exhaust the consider- 
ation of fallacy in general, for there are various species 
of false reasoning which may affect a whole train of 
syllogisms. These, — of which the Petitio P7nnci2Jii, 
the Ignoratio Elenchi, the Circidus, and the Saltiis m 
Concludendo, are the principal, — will be appropriately 
considered in the sequel, when we come to treat of the 
Doctrine of Probation or Demonstration. With Fal- 
lacies terminated the one Great Division of Pure Logic, 
— the Doctrine of Elements, or Stoicheiology, — and I 

VOL. II. A 



LECTURES ON LOGIC. 



LECT. opentlieotlierGreat Division, — the Doctrine of Method, 



XXIV 



or Methodology, — with the following paragraph. 



Par. Lxxx. IF LXXX. A Sciouce is a complement of cog- 

Method in . . , . . . /» -n 11 

genenij. mtions, havmg, m pomt oi i*orm, the character 

of Logical Perfection ; in point of Matter, the 
character of Real Truth. 

The constituent attributes of Logical Perfec- 
tion are the Perspicuity, the Completeness, the 
Harmony, of Knowledge. But the Perspicuity, 
Completeness, and Harmony of our cognitions 
are, for the human mind, possible only through 
Method. 

Method in general denotes a procedure in the 
treatment of an object, conducted according to 
determinate rules. Method, in reference to Sci- 
ence, denotes, therefore, the arrangement and ela- 
boration of cognitions according to definite rules, 
with the view of conferrino; on these a Looical 
Perfection. The Methods by which we proceed 
ill the treatment of the objects of our knowledge 
are two ; or rather Method, considered in its inte- 
grity, consists of two processes, — Analysis and 
Synthesis. 

1. The Analytic or Regressive ; — in which, de- 
parting from the individual and the determined, 
we ascend always to the more and more general, 
in order finally to attain to ultimate principles. 

IL The Synthetic or Progressive ; — in which 
we depart from principles or universals, and from 
these descend to the determined and the indi- 
vidual. 

Through the former we investigate and ascer- 
tain the reality of the several objects of science ; 



LECTURES ON LOGIC. 3 

tliroiio-li tlie latter we conuect the fragments of lect. 

. XXIV 

our knowledge into the unity of a system. — '- 

In its Stoicheiology or Doctrine of Elements, Logic Expiica- 
considers the conditions of possible thought : for thought Possibility 
can only be exerted under the general laws of Identity, faction of 
Contradiction, Excluded Middle, and Keason and Con- "''^^'*' 
sequent ; and through the general forms of Concepts, 
Judgments, and Keasonings. These, therefore, may 
be said to constitute the Elements of thought. But 
we may consider thought not merely as existing, but 
as existing Avell ; that is, we may consider it not only 
in its possil^ility, but in its perfection : and this per- 
fection, in so far as it is dependent on the form of 
thinking, is as much the object-matter of Logic as the 
mere possibility of thinking. Now that part of Logic 
which is conversant with the Perfection, — with the 
Well-being, of thought, is the Doctrine of Method, — 
Methodology. 

Method in general is the regulated procedure to- Method in 

-, .-,■,. -i ■■ general, — 

wards a certain end ; that is, a progress governed by what. 
rules which guide us by the shortest way straight 
towards a certain point, and guard us against devi- 
ous aberrations." Now the end of thought is truth, — 
knowledge, — science, — expressions which may here be 
considered as convertible. Science may, therefore, be Sciences- 
regarded as the perfection of thought, and to the 

a [On Method, see Alex. ApUrod., Peter John Nunnesius, De (Jonstita- 
In Anal. Prior. ,i.^'^,A\A.\52Q. Am- flone Artis Dialecticce,j). iZetseq.,ed. 
mon'ms, In P^'omn. Porphyrii,i. 21b, 1554, with relative commentary. Tim- 
Aid. 1546. Philoponus, In An. Prior., pier, Systema Logicce, L. iv. c. viii. p. 
f. 4. InAn.Post.,t9i. Eustratius, /h 716 et seq. G. Bownam, Commentarii 
^n.Po.s?.,fF.lb,53'\ See also Molinscus, in P. Raini Dialecticam, L. ii. c. 17, 
Zabarella, Nunnesius, Timpler, Dow- p. 472 et seq. On the distinction be- 
nam.] [MolinsiuB, Logica, L.ii.,i)e ilfe- tween Method and Order, see Lectures 
thodo, -p. 2i5 et seq. Zabarella, O/Jera on Metap}iysics,Yo\. i, lect. vi. p. 96, 
Logica, De Methndis, L. i. c. 2, p. 134. and note. — Ed.] 



4 LECTURES ON LOGIC. 

LECT. accomplislimeiit of tliis perfection the Metliodology of 

1 L. Logic must be accommodatecl and conducive. But 

Science, that is, a system of true or certain knowledge, 
Its pcrfec- supposes two couditions. Of these the first has a re- 
i.mi anT latiou to thc knowing subject, and supposes that w^hat 
is known is known clearly and distinctly, completely, 
and in connection. The second has a relation to the 
objects known, and supposes that what is known has 
a true or real existence. The former of these consti- 
tutes the Formal Perfection of science, the latter is the 
Material. 
Logic takes Now, as Logic is a science exclusively conversant 
only the""" about thc fomi of thought, it is evident that of these 
fecUon oT two couditious, — of these two elements, of science or 
perfect thinking, Logic can only take into account the 
formal perfection, which may, therefore, be distinc- 
tively denominated the logical perfection of thought. 
Logical Logical Methodology will, therefore, be the exposition 
o!oj?y°— of the rules and ways by which we attain the formal 

or logical perfection of thought. 
Method iu B^it Method, considered in general, — considered in 
Mstr™ two' i^s unrestricted universality, — consists of two processes, 
.nmUom-" correlative and complementary of each other. For 
jlocesses,- ^^ procccds either from the whole to the parts, or from 
™Tsyn- the parts to the whole. As proceeding from the whole 
to the parts, that is, as resolving, as unloosing, a com- 
plex totality into its constituent elements, it is Ana- 
lytic ; as proceeding from the parts to the whole, that 
is, as recomposing constituent elements into their 
complex totality, it is Synthetic. These two processes 
are not, in strict propriety, two several methods, but 
together constitute only a single method. Each alone 
is imperfect : — each is conditioned or consummated by 



tliesis 



LECTURES ON LOGIC. o 

the other : and, as I formerly observed," Analysis and lect. 

•^ 111 XXIV. 

Synthesis are as necessary to themselves and to the 

life of science, as expiration and inspiration in connec- 
tion are necessary to each other and to the possibility 
of animal existence. 

It is here proper to make you aware of the confusion Confusion 

T . . P T ^^ regard to 

which prevails in regard to the application of the terms the appiica- 

■"■ ' Q . f. . tion of the 

Analysis 2(iidi Synthesis.^ It is manifest, m general, terms Ana- 

-. • lysis Riici 

from the meaning of the words, that the term afialysis Synthesis. 
can only be applied to the separation of a whole into 
its parts, and that the term synthesis can only be ap- 
plied to the collection of parts into a whole. So far, 
no ambiguity is possible, — no room is left for abuse. 
But you are aware that there are different kinds of These couu- 

f 1 1 1 T 1 **'" pi'ocesses 

whole and parts ; and that some of the wholes, like as applied 

Ti/T to the coun- 

the whole of Comprehension, (called also the ikZeto- ter wholes 

1^ • /nil of Compre- 

physical), and the whole of Extension, (called also hension and 

'^ "^ . , , . • p 1 1 Extension, 

the Logical), are in the inverse ratio of each other : so correspond 



a See Lectures on Metaphysics, vol. particulars to uuiversals ; other logi- 

i. p. 99. — Ed. cians generally the reverse.] — [See 

/3 [Zabarella, Opera Logica, Lihcr de his Prcvcepta Phil. Loyicce, P. III. c, 

Reyressu, pp. 481, 489. See also, In i. §3, p. 84, 1781. — " Mentem suapte 

Anal. Poster., L. ii. text 81, pp. 1212, natura Syntheticam Methodum sequi, 

1213. MolinjBus, Lo/jica, L. ii. Ap- eaque ad universales ideas pervenire. 

peudix, p. 241 et seq., who notices .... Contrarium est iter Ana- 

that both the Analytic and Synthetic lyticse Methodi, quse ab universalibus 

order may proceed from the general initium ducit et ad peculiaria pro- 

to the particular. See also to the greditur, dividendo Genera iu suas 

same effect Hoff bauer, Uber die Ana- Formas." " Contra communem sen- 

hjsis in der Philosophic, p. 41 et sum et verborum naturam, Syntheti- 

seq., Halle, 1810. Gassendi, Pliy- cam vocant Methodum, qufe dividit, 

sica, Sectio iii. Memb. Part, L. ix. Analyticam contra, qua3 componit." 

Opera, t. ii. p. 460. Victorin, Neue Prasf. sub. fin. Iu the edition of the 

natilrlichere Darstellung der Logik, § Prcecepda by Maa,ss, Wyttenbach is 

214. Trendelenburg, £'fc;)ien to Zocy/ces made to say precisely the reverse of 

AristotcUrce, p. 89. Troxler, Logik, ii. what he lays down in the original 

p. 100, n.**. Krug,Zo(ifJi, §114, p. 406, edition. — See Prcec. Phil. Log., ed. 

u. **, and § 120, p. 431. Wyttenbach Maass, p. 64.— Ed.] 
makes Synthetic method progress from 



LECTURES ON LOGIC. 



LECT. 
XXIV. 



with cadi 
other. 



Hence the 
terms An- 
alysis and 
Synthesis 
used in a 
contrary 
sense. 



that what in the one is a part is necessarily in the 
other a whole. It is evident, then, that the counter 
processes of Analysis and Synthesis, as applied to these 
counter wholes and parts, should fall into one or cor- 
respond ; inasmuch as each in the one quantity should 
be diametrically opposite to itself in the other. Thus 
Analysis, as applied to Comprehension, is the reverse 
process of Analysis as applied to Extension, hut a 
corresponding process with Synthesis ; and vice versa. 
Now, should it happen that the existence and opposi- 
tion of the two quantities are not considered, — that 
men, viewing the whole of Extension or the whole of 
Comprehension, each to the exclusion of the other, 
must define Analysis and Synthesis with reference 
to that single quantity which they exclusively take 
into account ; — on this supposition, I say, it is mani- 
fest that, if different philosophers regard different 
wholes or quantities, we may have the terms analysis 
and synthesis absolutely used by different philosophers 
in a contrary or reverse sense. And this has actually 
happened. The ancients, in general, looking alone to 
the whole of Extension, use the terms analysts and 
analytic simply to denote a division of the genus into 
species, — of the species into individuals ; the moderns, 
on the other hand, in general, looking only at the 
whole of Comprehension, employ these terms to express 
a resolution of the individual into its various attri- 
butes.** But though the contrast in this respect 
between the ancients and moderns holds in general, 
still it is exposed to sundry exceptions ; for, in both 
periods, there are philosophers found at the same game 
of cross-purposes with their contemporaries as the 



a [See Aristotle, Physica, L. iv. c. i. qu. 1], p. 248.] 
3. Timpler, Lo<jka; Systema, L. ii. c. 



LECTURES ON LOGIC. 7 

ancients and moderns in 2:eneral are with each other, lect. 

XXIV 

This difference, which has never, as far as I know, been — '- 



fully observed and stated, is the cause of great con- 
fusion and mistake. It is proper, therefore, when we 
use these terms, to use them not in exclusive relation 
to one whole more than to another ; and at the same 
time to take care that we guard against the misappre- 
hension that might arise from the vague and one-sided 
view which is now universally prevalent. So much 
for the meaning of the words analytic and synthetic, 
which, by the way, I may notice, are, like most of our 
logical terms, taken from Geometry." 

The Synthetic Method is likewise called the Pro- The Synthe- 
gressive ; the Analytic is called the Regressive. Now has beeu 
it is plain that this application of the ievms j^rogressive Progressive, 

. . . aud the An- 

and 'regressive is aJtogether arbitrary, i^ or the import aiytic the 

„ . , , . " . . Regressive. 

01 these words expresses a relation to a certain point These desig- 
of departure, — a terminus a quo, and to a certain point "hoir/arii- 
of termination, — a terminus ad quern ; and if these o^vlrious 
have only an arbitrary existence, the correlative words "^"^^ '^'''^'""' 
will, consequently, only be of an arbitrary application. 
But it is manifest that the point of departure, — the 
point from which the Progressive process starts, — may 
be either the concrete realities of our experience, — the 
2:>rincipiata, — the notiora nobis; or the abstract gen- 
eralities of intelligence, — the lyrincipia, — the notiora 
natura. Each of these has an equal right to be re- 
garded as the starting-point. The Analytic process is 
chronologically first in the order of knowledge, and 
we may, therefore, reasonably call it the i:)rogressive, 
as starting from the primary data of our observation. 

a See above, vol. i. p. 279, n. ;8. — Philoponus, In An. Post., f. 36* 
Ed. [On theAnalj'sis of Geometry, see Veuet. 1534.] 
Plotinus, Ennead., iv. L. ix. c. 5. 



LECTURES ON LOGIC. 



LECT. 
XXIV. 



In general, 
Syutliosis 
has been 
designated 
tiie Progres 
sive, and 
Analysis 
the Regres- 
sive Pro- 
cess. 



Method in 
sjiecial. 



Oil the other hand the Synthetic process, as following 
the order of constitution, is first in the order of nature, 
and we may, therefore, likewise reasonably call it the 
2)rogressive, as starting from the primary elements of 
existence. The application of these terms as syno- 
nyms of the analytic and synthetic processes, is, as 
wholly arbitrary, manifestly open to confusion and 
contradiction. And such has been the case. I find 
that the philosophers are as much at cross-purposes in 
their application of these terms to the Analytic and 
Synthetic processes, as in the application of analysis 
and synthesis to the different wholes. 

In general, however, both in ancient and modern 
times, Synthesis has been called the Progressive, 
Analysis the Regressive, process ; an application of 
terms which has probably taken its rise from a pas- 
sage in Aristotle, who says, that there are two ways 
of scientific procedure, — the one from principles (0,770 
T(ov ap^(xiv), the other to principles, (eVt ra? ap\a<^.) 
From this and from another similar passage in 
Plato (?) the term pi'ogressive has been applied to the 
process of Comprehensive Synthesis, [progrediendi a 
2orincipiis ad jjrincipiata), the term regressive, to the 
process of Comprehensive Analysis, (lyrogrediendi a 
pinncipiatis ad principia.) " 

So much for the general relations of Method to 
thought, and the general constituents of Method itself 
It now remains to consider what are the particular 



a Eth. Nic, i. 2 (4). The reference 
to Plato, whom Aristotle mentions as 
making a similar distinction, is pro- 
bably to be fouii% \y^ comparing two 
separate passages- irf'' the Republic, B. 
iv. p. 435, vi. p. 504. — Ed. [Plato is 
said to have taught Analysis to Leoda- 
mas the Thasian. See Laertius, L. iii. 



24, and Proclus, quoted in Is. Casau- 
bon's note. On the views of Method of 
Aristotle and Plato, see Scheibler and 
Dowuam.] [Scheibler, Opera Logica, 
Pars iv., Tract. Si/llog., c. xviii., De 
Methodo, tit. 7, p. 603. Downam, Co7n. 
in P. Rami Dialecticam, L. ii. c. 1 7, p. 
482.— Ed.] 



LECTUE-ES ON LOGIC. 9 

applications of Method, by wliich Logic accomplishes lect. 
the Formal Perfection of thought. In doing this, it is — - — 1- 
evident that, if the formal perfection of thought is 
made up of various virtues, Logic must accommodate 
its method to the acquisition of these in detail ; and 
that the various processes by which these several 
virtues are acquired, will in their union constitute the 
system of Logical Methodology. On this I will give 
you a paragraph. 

H LXXXL The Formal Perfection of thought Par. lxxxi. 
is made up of the three virtues or characters : — MeUiod- 
1°, Of Clearness; 2°, Of Distinctness, involving Three' Parts. 
Completeness; and, 3°, Of Hannonij. The char- 
acter of Clearness depends principally on the de- 
termination of the Comprehension of our notions; 
the character of Distinctness depends principally 
on the development of the Extension of our 
notions ; and the character of Harmony, on the 
mutual Concatenation of our notions. The rules 
by which these three conditions are fulfilled, con- 
stitute the Three Parts of Logical Methodology. 
Of these, the first constitutes the Doctrine of 
Dejinition; the second, the Doctrine of Division; 
and the third, the Doctrine of Probation. °' 



a Kriig, Loi/ik, § 121". — Ed. [Ra- mascus speaks strongly of Method in 

mus was the first to inti'oduce Method his Dialectic, ch. G8, and makes four spe- 

as a part of Logic under Syllogistic, cial logical methods, Division, Defini- 

(see his Dialectica, L. ii. c. 17), and tion, Analysis, Demonstration. Eusta- 

the Poi't Royalists, (1662), made it a chius treats of Method under Judg- 

f ourth part of logic. See La Lor/ique ment, and Scheibler under Syllogistic] 

ou L'Art dc Pcnser, Prem. Dis., i>. 26, [Eustachius, Summa Pliilosophice, Lo- 

pp. 47, 50. Quat. Part., p. 445 et seq. gica, P. ii. Tract. 2. De Methodo, p. 

ed. 1775. Gassendi, in his Institutio 106, ed. Lugd. Batav., 1747. First 

Logica, has Pars iv., De Methcdo. edition, 1609. Scheibler, 0/Je»'a i or/ j- 

He died in 1655 ; his Logic appeared ca, Pars iv. c. xviii. p. 69o et seq. — 

posthumously in 1658. John of Da- Ed.] 



10 LECTURES ON LOGIC. 

LECT. "When we turn attention on our tbouo-lits, and 

XXIV 

(leal with them to the end that they may be consti- 



don ^'"'^ tuted into a scientific whole, we must perform a three- 
fold operation. We must, first of all, consider what 
we think, that is, what is comprehended in a thought. 
In the second place, we must consider how many 
things we think of, that is, to how many objects the 
thought extends or reaches, that is, how many are 
conceived under it. In the third place, we must con- 
sider why we think so and so, and not in any other 
manner ; in other words, how the thoughts are bound 
together as reasons and consequents. The first con- 
sideration, therefore, regards the comprehension ; the 
second, the extension ; the third, the concatenation of 
our thoughts. But the comprehension is ascertained 
by definitions ; the extension by divisions ; and the 
concatenation by probations." " We proceed, therefore, 
to consider these Three Parts of Lomcal Methodoloo;v 
in detail ; and first, of Declaration or Definition, in 
regard to which I give the following paragraph. 

Par. Lxxxii. ^ LXXXII. How to make a notion Clear, is 

trine'of De- showu by thc logical doctrine of Declaration, or 

and Defini- Definition in its wider sense. A Declaration, (or 

Definition in its wider sense), is a Categorical 
Proposition, consisting of two clauses or members, 
viz. of a Subject Defined, {memhrum definitum), 
and of the Defining Attributes of the subject, that 
is, those by which it is distinguished from other 
things, {rnemhrutn dejinieus). This latter mem- 
ber really contains the Definition, and is often 
itself so denominated. Simple notions, as con- 

a Krug, Logilc, § 121'''. — Ed. 



LECTURES ON LOGIC. 11 

taining no plurality of attributes, are incapable lect. 
of definition." 1 



The terms declaration and dejinition, which are here Expiica- 
used as applicable to the same process, express it, xiie terms 
however, in different aspects. The term declaration , and Defini- 
(declaratio), is a word somewhat vaguely employed inthTsamJ^^* 
English ; it is here used strictly in its proper sense a^fferenr 
of throwing light upo7i, — clearing up. The term defini- ^^^"^ ^' 
tion, (definitio), is employed in a more general, and in 
a more special, signification. Of the latter we are soon 
to speak. At present, it is used simply in the meaning 
of an enclosi7ig ivithin limits, — the separating a thing 
from others. AVere the term declaration not of so vague 
and vacillating a sense, it would be better to employ it 
alone in the more general acceptation, and to reserve 
the term dejinition for the special signification. 

T LXXXIII. The process of Definition is Par.Lxxxin. 

,-,.■,,. f»ri T • Definition 

founded on the logical relations oi Subordination, in its stricter 

sense, — 

Co-ordination, and Congruence. To this end we what, 
discriminate the constituent characters of a no- 
tion into the Essential, or those which belong to 
it in its unrestricted universality, and into the 
Unessential, or those which belong to some only 
of its species. The Essential are again discrim- 
inated into Original and Derivative, a division 
which coincides with that into Internal or Pro- 
per, and External. In giving the sum of the 
original characters constituent of a notion, con- 
sists its Definition in the stricter sense. A De- 
finition in the stricter sense must consequently 

a Ki-ug, Lwjik, § 121b.— Ed. 



12 LECTURES ON LOGIC. 

LECT. afford at least two, and properly only two, ori- 

-I-1_J- pinal characters, viz. that of the Genus imme- 



diately superior, {genus iwoximum), and that of 
the Difference by which it is itself marked out 
from its co-ordinates as a distinct species, {iiota 
specialis, differentia specifica) « 

Expiica- Declarations (or definitions in the wider sense), ob- 

Various talu various denominations, according as the process 
Declaration, is performed in different manners and degrees. A 
Expiica- Declaration is called an Explication, (explicatio), when 
the predicate or defining member indeterminately 
evolves only some of the characters belonging to the 
Exposition, subject. It is called nji Exposition, {expositio), when 
the evolution of a notion is continued through several 
Description. expHcatious. It is called a Description, [descriptio), 
when the subject is made known through a number of 
Definition coucretc characteristics. Finally, it is called a Defi- 
nition Proper, when, as I have said, two of the essen- 
tial and original attributes of the defined subject are 
given, whereof the one is common to it with the 
various species of the same genus, and the other dis- 
criminates it from these.^ 
Definitions, " Defiuitlous arc distinguished also into Verbal or 
Reai°"ud ' Nominal, into Eeal, and into Genetic, [definitiones no- 
minales, reales, geneticce), according as they are con- 
versant with the meaning of a term, with the nature 
of a thing, or with its rise or production.''' Nominal 
Definitions are, it is evident, merely explications. 
They are, therefore, in general only used as prelim- 
inary, in order to prepare the way for more perfect 

a [Cf. Arif3totle, Topka, i. 6. Keck- Logik, p. 94.] 

ermaun, Si/stema Logicce Minus, L. i. j8 Cf. Krug, Logil; § 122. — Ed. 

c. 17. Opera, t. i. pp. 199, 656. y [Cf. Eeusch, Systema Loglcum, § 

Scheibler, To2nca, c. 30. Richter, 309 et scq.] 



LECTURES ON LOGIC. 13 

declarations. In Eeal Definitions the thing defined is lect. 

considered as already there, as existing (ov), and the .U 1 

notion, therefore, as given, precedes the definition. 
They are thus merely analytic, that is, nothing is 
given explicitly in the predicate or defining member, 
which is not contained implicitly in the subject or 
member defined. In Genetic Definitions the defined 
subject is considered as in the progress to be, as be- 
coming iyiyvoixevov) ; the notion, therefore, has to be 
made, and is the result of the definition, which is con- 
sequently synthetic, that is, places in the predicate or 
defining member more than is given in the subject or 
member defined. As examples of these three species, 
the following three definitions of a circle may suffice : — 
1. The Nominal Definition, — The word circle signifies 
an uniformly curved line. 2. The Real Definition, — 
A circle is a line returning upon itself, of which all 
the parts are equidistant from a given point. 3. The 
Genetic Definition, — A circle is formed when we draw 
around, and always at the same distance from, a fixed 
point, a movable point w^hich leaves its trace, until 
the termination of the movement coincides with the 
commencement.* It is to be observed that only those 
notions can be genetically defined, which relate to 
quantities represented in time and sj^ace. Mathema- 
tics are princijDally conversant with such notions, and 
it is to be noticed that the mathematician usually de- 
nominates such genetic definitions real definitions, 
while the others he calls without distinction nominal 
definitions!' ^ 

The laws of Definition are given in the following 
paragraph. 

a This example is taken, with some ;8 Krug, Zo'///,-, § 122. Aniii. 3, pp. 
alteration, from Wolf, PhUosojihia 448, 449. — Ed. 
ItatlonaVis, % 191.— Ed. 



14 LECTURES ON LOGIC. 

LECT. T LXXXIV. A definition should be Adequate 

— L (adequata), that is, the subject defined, and the 

Par. LXXXIV, predicate defining, should be equivalent or of the 

Definition, . _„ - . _ ., ^. 

—its Laws. same extension, it not, the sphere oi the predi- 

cate is either less than that of the subject, and 
the definition Too Narrow, {angustior), or greater, 
and the definition Too Wide (latior). 

II. It should not define by Negative or Divi- 
sive attributes, {Ne sit negaus, ne flat j9er dis- 
juncta). 

III. It should not be Tautological, — what is 
contained in the defined, should not be repeated 
in tlie defining clause, {Ne sit circvlus vel dicdlelon 
m definiendo). 

IV. It should be Precise, that is, contain no- 
thing unessential, nothing suj^erfluous, {Definitio 
ne sit abundans). 

V. It should be Perspicuous, that is, couched 
in terms intelligible, and not figurative, but 
proper and compendious." 

Expiica- The First of these rules : — That the definition should 

tiou. 

First Rule, bc adcquatc, that is, that the dcfinieiis and definitum 
should be of the same extension, is too manifest to 
require much commentary. Is the definition too 
wide"? — then more is declared than ouoht to be 
declared ; is it too narrow '? — then less is declared 
than ought to be declared ; — and, in either case, the 
definition does not fully accomplish the end which it 
proposes. To avoid this defect in definition, we must 
attend to two conditions. In the first place, that 

a Of. Kvug, Logih, § 123. — Ed. nitione, Oxiera,^^. Qi?> et xeq. Buffier, 

[Victorin, Logik, § 223 ct seq. Sig- Veritez de Consequence, %i5-51. Gocle- 

wart, JIandbut'h zu, Vorlemngen ilber nius, Lexicon, Philosophiciim, v. Defin- 

die Lotjik, § 371. Boethius, De Defi- itio, p. 500.] 



LECTURES ON LOGIC. 15 

.ittribute should be given which the thinsr defined lect. 

. XXIV 

has in common with others of the same class ; and, in '- 



the second j^lace, that attribute should be given which 
not only distinguishes it in general from all other 
things, but proximately from things which are in- 
cluded with it under a common class. This is ex- 
23ressed by Logicians in the rule — Definitio constet 
genere 2^^'oximo et diferentia ultima, — Let the defin- 
ition consist of the nearest genus and of the lowest 
difference. But as the notion and its definition, if this 
rule be obeyed, are necessarily identical or convertible 
notions, they must necessarily have the same extent ; 
consequently, everything to which the definition ap- 
plies, and nothing to which it does not apply, is the 
thing defined. Thus ; — if the definition, Man is a 
rational animal, be adequate, we shall be able to say 
— Every rational animal is human : — nothing ichich 
is not a rational animal is human. But we cannot say 
this, for though this may be true of this earth, we can 
conceive in other worlds rational animals which are 
not human. The definition is, therefore, in this case 
too wide ; to make it adequate, it will be necessary to 
add terrestrial or some such term — as, Man is a ra- 
tional animal of this earth. Again, were we to define 
Man, — a rationally acting animal of this earth, — the 
definition would be too narrow ; for it would be false 
to say, no animal of this earth not acting rationally is 
human, for not only children, but many adult persons, 
would be excluded by this definition, which is, there- 
fore, too narrow." 

The Second Rule is, — That the definition should not second 
be made by negations, or disjunctions. In regard to 
the former, — negations, — that we should define a thing 

a Cf. Krug, Lotj'tl-, % 123. Aiini. i.^Ec 



iscTTSE? OS tiwac 



XXTf 



i>f it. 



nvgi.^ 



X3Er;Z3:H2= 



IZ'ITTEES OS UjGIC. 17 

to assnie ns. Bnt a de£il:i'-- by dUpaiaze aixecL^- lect. 

lives is, thongh. it mav Taz^e^r circnmsciibe a no^icaii, 1 

only to Ve 'Musiiered as a prelii=':»ry deirnTtJoiL and 
as ihr _ LT and yet inipQ^ecx knov- 

led^. >'» r most not. no^'eTer, confoon^. dc^DiticHis 
by 'iivisive arrritz.'.-is -sitb propoeitioiis eipre^ve of 
a divisioii. 

TLeTl:: :._r is-— T-- _ . . 

tantologicai ; tiiat is. 

defined by itseli Ti-is tic'z ir -j De^bea 

Circle. This mlf ' ~ r - .-* 

or mediately. T.^ - 

memd, — ^is an ex;:.!- - : - Ar^^ 

diate cirde requires, at least, xwa 

itioDS, a pdndpsd smd a safaEadiazy. i — 

Lair is the expressed iris4 <^' a ruler, 

one tcho estabGghes laits. Tbe drde. 

diate or mediate, is manifest or o: _ 

the things defined is reiieated in tl 

^i-ith other synonynioos vordr 

example it was manifest- In tl : _ 

cealed : — Gratitude is a nrtue — 

BigJit is Ae competence to do or hid to do. Sodi 

dedaiations may. however, be aDoved t 

lusoiy or ncHninal definitions^ Ccaiceal^ 

finitions are of very ^- "fnt ocerarez-- ___ :__ 

aie at iiie same tim; :? ox remote : for we «rr 

very apt to aUoir ourselves to l:«e deceived by :L 

ferenee of explosion, and &ncy that we 

a notion when we have oiii~ ~r t . p — ^- 

We ought, therefoxe, to l«r -- _ ^5 izsirst 

this besetting vice. TL: 

definition also by tl : i :l5 iz uiis 

case we declaie the *i<ii 

VOL II. z 



18 LECTURES ON LOGIC. 

LECT. procally by each otlier (St' dWajXcovy. In probation 
'- there is a similar vice which bears the same names."^ 



We may, I think, call them by the homely English 
appellation of the Seesatv. — 
Fourth The Fourth Rule is, — " That the definition should be 

precise ; that is, contain nothing unessential, nothing 
superfluous. Unessential or contingent attributes are 
not sufficiently characteristic, and as they are now 
present, now absent, and may likewise be met with in 
other things which are not comprehended under the 
notion to be defined, they, consequently, if admitted 
into a definition, render it sometimes too wide, some- 
times too narrow. The well-known Platonic defini- 
tion, — ' Man is a two-legged animal without feathers,' 
■ — could, as containing only unessential characters, be 
easily refuted, as was done by a plucked cock.'^ And 
when a definition is not wholly made up of such attri- 
butes, and when, in consequence of their intermixture 
with essential characters, the definition does not abso- 
lutely fail, still there is a sin committed against logical 
purity or precision, in assuming into the declaration 
qualities such as do not determinately designate what 
is defined. On the same principle, all derivative cha- 
racters ought to be excluded from the definition ; for 
although they may necessarily belong to the thing 
defined, still they overlay the declaration with super- 
fluous accessories, inasmuch as such characters do not 
designate the original essence of the thing, but are a 
mere consequence thereof. This fault is committed in 
the following definition : — The Circle is a curved line 
returning upon itself, thej^arts ofivhich are at an equal 

a Compare SextusEmpiricus,P^V'')'/(. ^ Krug, Logik, § 123. Anm. 3. — 
//y/:i., i. 169, ii. C8.— Ed. " Ed. 

7 Diog. Laert., \'i. 40. — Ed. 



LECTURES ON LOGIC. 19 

distance from the central point. Here precision is vio- lect, 
lated, though the definition be otherwise correct. For — '- 



that every line returning upon itself is curved, and 
that the point from which all the parts of the line are 
equidistant is the central point, — these are mere con- 
sequences of the returning on itself, and of the equi- 
distance. Derivative characters are thus mixed up 
with the original, and the definition, therefore, is not 
precise." '^ 

The Fifth Kule is, — " That the definition should be Fifth Rule, 
perspicuous, that is, couched in terms intelligible, not 
figurative, and compendious. That definitions ought 
to be perspicuous, is self-evident. For why do we de- 
clare or define at all 1 The perspicuity of the defini- in order to 

1 -\ • ^ n 1 i'iT-11 perspicuity 

tion depends, m the first place, on the intellio;ible in Defini- 

1 PIT 11- -1 ? tion, 1. The 

character oi the language, and this again depends on language 
the employment of words in their received or ordinary intelligible. 
signification. The meaning of words, both separate 
and in conjunction, is already determined by conven- 
tional usage ; when, therefore, we hear or read these^ 
we naturally associate with them their ordinary mean- 
ing. Misconceptions of every kind must, therefore, 
arise from a deviation from the accustomed usage ; 
and though the definition, in the sense of the definer, 
may be correct, still false conceptions are almost in- 
evitable for others. If such a deviation becomes neces- 
sary, in consequence of the common meaning attached 
to certain words not corresponding to certain notions, 
there ought at least to be appended a comment or 
nominal definition, by which we shall be warned that 
such words are used in an acceptation wider or more 
restricted than they obtain in ordinary usage. But, in 

o Krug, Locjil; § 123. Anm. 2.— Ed. 



20 LECTURES ON LOGIC. 

LECT. the second place, words ought not only to be used in 

^^^^' their usual signification, — that signification, if the de- 

melning finitiou bo perspicuous, must not be figurative but 



must be not pj-Qpgp^ Tropcs aud figures are logical hieroglyphics, 



meaning 
must be E 
figurative 

but proper. ^^^ thcmselves require a declaration. They do not 
indicate the thing itself, but only something similar."" 
Such, for example, are the definitions we have of Lo- 
gic as the Pharus Intellectus, — the Lighthouse of the 
Understanding, — the Cynosura Veritatis, — the Cpio- 
sure of Truth, — the Medicina Mentis, — the Physic of 
the Mind, &c.^ 

" However, many expressions, originally metapho- 
rical, (such as conception, imagination, comprehension, 
representation, kc. &c.), have by usage been long since 
reduced from figurative to proper terms, so that we 
may em^^loy these in definitions without scruple, — 
nay frequently must, as there are no others to be 
found. 

3 The defi- " jj^ ^l^g third place, the perspicuity of a definition 

mtion must ■•• ■•• J- -^ 

be brief, depends upon its brevity. A long definition is not 
only burthensome to the memory, but likewise to the 
understanding, which ought to comprehend it at a 
single jet. Brevity ought not, however, to be pur- 
chased at the expense of perspicuity or completeness."''' 

The other " Thc rulcs hithcrto considered, proximatelv relate to 

kinds of T^£•• • ^ • r ^ 

Declaration. Deilmtions ID. the strictcr sense. In reference to the 

other kinds of Declaration, there are certain modifica- 

Diiucida- tions and exceptions admitted. These Dilucidations 

tions or Ex- . 

plications, or Jlixplications, as they make no pretence to logical 
perfection, and are only subsidiary to the discovery of 
more perfect definitions, are not to be very rigidly 
dealt with. They are useful, provided they contain 

a Krug, Logik, § 123. Anm. 4.— & See above, vol. i. y>- 3.5.— Ed. 
Ed. 7 Krug, tVj/f/.— Ed. 



LECTURES ON LOGIC. 21 

even a sinoile time character, by which we are con- lect. 

^ ' -^ XXIV. 



ducted to the apprehension of others. They may, 
therefore, be sometimes too wide, sometimes too nar- 
row. A contingent and derivative character may be 
also useful for the discovery of the essential and ori- 
ginal. Even Circular Definitions are not here abso- circular 

~ _ . Definitions. 

lately to be condemned, if thereby the language is 
rendered simpler and clearer. Figiu-ative Expressions Figurative 
are likewise in them less faulty than in definitions sions. 
proper, inasmuch as such expressions, by the analogies 
they suggest, contribute always something to the illus- 
tration of the notion. 

" In regard to Descriptions, these must be adequate, Descrip- 
and no circle is permitted in them. But they need 
not be so precise as to admit of no derivative or con- 
tingent characters. For descriptions ought to enume- 
rate the characters of a thing as fully as possible ; and, 
consequently, they cannot be so brief as definitions. 
They cannot, however, exceed a certain measure in 
point of length."" 

o Ki-ug, Lorjih, § 123. Anm. 5. — Eu. 



22 LECTURES ON LOGIC. 



LECTURE XXV. 

METHODOLOGY. 

SECTION II. — LOGICAL METHODOLOGY. 

II. — DOCTRINE OF DIVISION. 

LECT. I NOW proceed to tlie Second Chapter of Logical 



Division. 



Methodology, — the Doctrine of Division, — the doctrine 
which affords us the rules of that branch of Method, 
by which we render our knowledge more distinct and 
exhaustive. I shall preface the subject of Logical 
Division by some observations on Division in general. 
Division in " Under Division (cUvisio, Statpecrts) we understand 

general. . . ^ . . 

in general the sundering of a whole into its parts.* 
The object which is divided is called the divided whole 
{totum divisum), and this whole must be a connected 
many, — a connected multiplicity, for otherwise no 
division would be possible. The divided whole must 
comprise at least one character, affording the condition 
of a certain possible splitting of the object, or through 
which a certain opposition of the object becomes 
recognised ; and this character must be an essential 
attribute of the object, if the division be not aimless 
and without utility. This point of view, from which 
alone the division is possible, is called the principle of 
the division {principiimi sive fundamentum divisi- 

a [On Division and its various kinds, f. 6^, Aid. 1546.] 
see Ammonias, Be Qiiinque Vocibus, 



LECTURES ON LOGIC. 23 

onis) ; and the parts which, by the distraction of the lect. 
whole, come into view, are called the divisive memhers — — 1- 
{membra dividentia). When a whole is divided into 
its parts, these parts may, either all or some, be them- 
selves still connected multiplicities ; and if these are 
again divided, there results a subdivision {suhdivisio), 
the several parts of which are called the suhdivisive 
7ne7nhers {me^nhi^a suhdividentia). One and the same 
object may, likewise, be differently divided from dif- 
ferent points of view, whereby condivisions {condivisi- 
ones) arise, which, taken together, are all reciprocally 
co-ordinated. If a division has only two members, it is 
called a dichotomy {dichotomia) ; if three, a trichotomy 
(trichotomia) ; if four, a tetrachotomy ; if many, a 
2^olytomy, &c. 

" Division, as a genus, is divided into two species. Division of 
according to the different kind of whole which it sun- -^PaTikTon 
ders into parts." These parts are either contained in Divisir 
the divided whole, or they are contained under it. In 
the former case the division is called a, 2^ci)tition {par- 
titio, a7rapWix7)(rii),^ in the latter, it is named a logical 
division? Partition finds an application only when 
the object to be divided is a whole compounded of 
parts, — consequently, where the notion of the object 
is a complex one ; Logical Division, on the other hand, 
finds its application only where the notion contains a 
plurality of characters under it, and where, conse- 
quently, the notion is an universal one. The simple 

a [On various kinds of Wholes, see a subject into successive heads, first, 

Caramuel, Jiationalis et Realis Philo- second, &c. See Hermogenes, Ilepl 

sojohia, L. iv. sect. iii. disp. iv. p. 277,] iSecav. Rhetores Grceci, i. p. 104, ed. 

[and above. Lectures on M elaphysics, Aid. — Ed. 

vol. ii. p. 340 ; Lectures onLor/ic, vol. i. y [See Keckermaian, SystemaLogicce, 

p. 201 Ed.] L. i. c. 3. Opera, t. i. p. 667. Dro- 

^'Airapieixria-is is properly a rhetori- bisch, ^^eue Darstellunfj der Logik,% 

cal term, and signifies the division of 112. Krug, Logik, § 124. Anm. 2.] 



24 LECTURES ON LOGIC. 

LECT. notion is thus the limit of Partition ; and the indi- 

'^'^^' vidual or singuLar is thus the limit of Division. Par- 

Partition titlou is divldcd into a physical or real, when the 

either Real j. i/ 

or Ideal, parts can actually be separated from each other ; and 
into a metaphysical or ideal, when the parts can only 
be sundered by Abstraction." It may be applied in 
order to attain to a clear knowledge of the whole, or 
to a clear knowledge of the parts. In the former case, 
the parts are given and the whole is sought ; in the 
latter, the whole is given and the parts are sought. 
If the whole be given and the parts sought out, the 
object is first of all separated into its proximate, and, 
thereafter, into its remoter parts, until either any 
further partition is impossible, or the partition has 
attained its end. To this there is, however, required 
an accurate knowledge of the object, of its parts proxi- 
mate and remote, and of the connection of these parts 
together, as constituting the whole. We must, like- 
wise, take heed whether the partition be not deter- 
mined from some particular point of view, in conse- 
quence of which the notions of more proximate and 
more remote may be very vague and undetermined. 

a By Partition, triangle maj' be dis- celes, and scalene. (The dichotomic 

tiuguished, 1 °, Into a certain portion division would, however, be here more 

'of space included within certain bound- proper.) By i-eference to the angles, 

aries ; 2°, Into sides and angles ; 3°, they are divided into the three species 

Into two triangles, or into a trapezium of rectangular, i.e. triangle which has 

and a triangle. The first two pai'ti- one of its angles right ; into ambly- 

tions are ideal, they cannot be actually gon, or ti'iangle which has one of its 

accomplished. The last is real, it may. angles obtuse; and into oxygon, /. c. 

By Division, triangle is distinguish- triangle which has its three angles 

ed, 1°, Into the two species of recti- acute. 

linear and curvilinear. 2°, Both of By Definition, triangle is distiu- 

these are again subdivided (A) by guished into figure of three sides, 

reference to the sides, (B) by refer- equal to triangular figure ; that is, 

euce to the angles. By reference to into figure, the proximate genus, and 

the sides, triangles are divided into trilateral or three-sided, the differen- 

the three species of equilateral, isos- iial quality. 



LECTURES ON LOGIC. 25 

If the parts be given, and from them the whole sought lect. 

out, this is accomplished when we have discovered the — 

order, — the arrangement, of the parts ; and this again 
is discovered when the principle of division is dis- 
covered ; and of this we must obtain a knowledge, 
either from the general nature of the thing, or from 
the particular end we have in view. If, for example, 
a multitude of books of every various kind are arranged 
into the whole of a weU-ordered library ; — in this case 
the greater or lesser similarity of subject will afford, 
either exclusively or mainly, the principle of division. 
It happens, however, not unfrequently, that the parts 
are ordered or arranged according to different rules, 
and by them connected into a whole ; and, in this 
case, as the different rules of the arrangement 
cannot together and at once accomplish this, it is 
proper that the less important arrangement should 
yield to the more important ; as, for example, in the 
ordering of a library, when, besides the contents of 
the books, we take into account their language, size, 
antiquity, binding, &C.'"' 

I now proceed to Logical Division, on which I give 
you the following paragraph : — • 

H LXXXV. The Distinctness and Completeness Par. lxxxv, 
of our knowledge is obtained by that logical pro- DiSn. 
cess which is termed Division (divisio, Statpeo-t?). 
Division supposes the knowledge of the w'hole to 
be given through a foregone process of Definition 
or Declaration ; and proposes to discover the 
parts of this whole which are found and deter- 
mined not by the development of the Comprehen- 
sion, but by the development of the Extension. 

a Esser, Logik, §§ 134, 135, p. 2G1-64.— Eu. 



2G LECTURES ON LOGIC. 

i-ECT. As Logical Definition, therefore, proposes to ren- 

— ^- — — der the cliaracters contained in an object, that 

is, the comprehension of a reality or notion, 
Clear ; Logical Division proposes to render the 
characters contained under an object, that is, the 
extension of a notion. Distinct and Exhaustive. 
Division is, therefore, the evolution of the exten- 
sion of a notion ; and it is expressed in a dis- 
junctive proposition, of which the notion divided 
constitutes the subject, and the notions contained 
under it, the predicate. It is, therefore, regu- 
lated by the law which governs Disjunctive 
Judgments, (the Principle of Excluded Middle), 
although it is usually expressed in the form of a 
Copulative Categorical Judgment. The rules by 
which this process is regulated are seven : — 

1°. Every Division should be governed by 
some principle, (Divisio ne caveat fundamento). 

2°. Every Division should be governed by only 
a single principle, 

3°. The principle of Division should be an 
actual and essential character of the divided 
notion, and the division, therefore, neither com- 
plex nor without a purpose. 

4°. No dividing member of the predicate must 
by itself exhaust the subject. 

5°. The dividing members, taken together, 
must exhaust, but only exhaust, the subject. 

6°. The divisive members must be reciprocally 
exclusive. 

7°. The divisions must proceed continuously 
from immediate to mediate differences, {Divisio 
nejiat 2^er saltum). 



LECTURES ON LOGIC. 27 

In tliis paragraph are contained, first, the general lect, 



XXV. 



Principles of Logical Division, and, secondly, the Laws 

by which it is governed. I shall now illustrate these tiou. ""^ 

in detail. 

In the first place, it is stated that " the distinct- 
ness and completeness of our knowledge is obtained 
by that logical process which is termed Division 
[divisio, Statpeo-t?). Division supposes the know- 
ledge of the whole to be given through a foregone 
process of definition, and proposes to discover the 
parts of this whole which are found and determined 
not by the development of the comprehension, but 
by the development of the extension. As logical 
definition, therefore, proposes to render the characters 
contained in a notion, that is, its comprehension, clear; 
logical division proposes to render the characters con- 
tained under an object, that is, the extension of a 
notioD, distinct. Division is, therefore, the evolution 
of the extension of a notion, and it is expressed in a 
disjunctive proposition, of which the notion divided 
constitutes the subject, and the notions contained 
under it, the predicate. It is, therefore, regulated by 
the law which governs disjunctive judgments (the 
principle of excluded middle), although it be usually 
expressed in the form of a copulative categorical 
judgment." 

The special virtue, — the particular element, of per- Endof Divi- 

. . . . sion is Dis- 

fect thmkmo', which Division enables us to acquire, tinctness, 

-P^ 1 • • • • 1 i which in- 

is Distinctness, but, at the same time, it is evident vohes 

. T 1 1 • • 1 1 • Complete- 

that it cannot accomplish this without rendering ness. 

our thinking more complete. This, however, is only 

a secondary and collateral result ; for the problem 

which division proximately and principally proposes 



28 LECTURES ON LOGIC. 

LECT. to solve is, — to afford us a distinct consciousness of 

L the extension of a given notion, tlirough a complete 

or exhaustive series of subordinate or co-ordinate 
notions. This utility of Division, in rendering our 
knowledge more complete, is, I find, stated by Aris- 
totle,'' though it has been overlooked by subsequent 
logicians. He observes that it is only by a regular 
division that we can be assured, that nothing has been 
omitted in the definition of a thing. 
As many " As it Is by mcaus of division that we discover 
Division what are the characters contained under the notion of 
there are au objcct, it follows that there must be as many kinds 
affording a of divislou posslblc as there are characters contained 
Division, under the notion of an object, wdiich may afibrd the 
principle of a different division. If the characters 
which aff'ord the principle of a division are only ex- 
ternal and contingent, there is a division in the wider 
sense ; if, again, they are internal and constant, there 
is a division in the stricter sense ; if, finally, they are 
not only internal but also essential and original, there 
A universal is a dlvlsiou ID. tlic strictcst scusc. From the very 

notion tlie . „,.,-,... . . 

only object conceptiou of lo^ical division, it is manifest that it 

of Logical ^ 1- 1 1 • 

Division, can only be applied where the object to be divided is 
a universal notion, and that it is wholly inapplicable 
to an individual ; for as the individual contains no- 
thing under it, consequently it is not susceptible of 

General ail ultcrior divlsiou. The efeneral problem of which 

problem of . . , ox 

Division, division affords the solution is, — To find the subor- 
dinate genera and species, the higher or generic notion 
being given. The higher notion is always something 
abstracted, — something generalised from the lower 
notions, with which it agrees, inasmuch as it contains 
all that is common to these inferior concepts, and from 

a Anal. Post., L. ii. c. 13. 



LECTURES ON LOGIC. 29 

which it differs, inasmuch as they contain a greater lect. 

number of determinino' characters. There thus sub- 

sists an internal connection between the higher and 
the lower concepts, and there is thus afforded a tran- 
sition from the superior notion to the subordinate, 
and, consequently, an evolution of the lower notions 
from the higher. In order to discover the inferior 
genera and species, we have only to discover those 
characters which afford the proximate determinations, 
by which the sphere or extension of the higher notion 
is circumscribed. But to find what characters are 
wanted for the thorough -going determination of a 
higher notion, we must previously know what char- 
acters the higher notion actually contains, and this 
knowledge is only attainable by an analysis, — a sund- 
ering of the higher notion itself. In doing this, the 
several characters must be separately drawn forth and 
considered ; and in regard to each, we must ascertain 
how far it must still be left undetermined, and how 
far it is capable of opposite determinations. But 
whether a character be still undetermined, and of 
what opposite determinations it is capable, — on these 
points it is impossible to decide a priori, but only 
a ])osteriori, through a knowledge of this particular 
character and its relations to other notions. And the 
accomplishment of this is rendered easier by two 
circumstances ; — the one, that the generic notion is 
never altogether abstract, but always realised and held 
fast by some concrete form of imagination ; — the 
other, that, in general, we are more or less acquainted 
with a greater or a smaller number of special notions, 
in which the generic notion is comprehended, and 
these are able to lead us either mediately or imme- 
diately to other subordinate concepts. 



,30 LECTURES ON LOGIC. 

LECT. " But tlie determinations or constituent cliaracters 
. L of a notion which we seek out, must not only be com- 
pletely, but also precisely, opposed. Completely, in- 
asmuch as all the species subordinate to the notions 
ought to be discovered ; and precisely, inasmuch as 
whatever is not actually a subordinate species, ought 
to be absolutely excluded from the notion of the 
genus. 

" In regard to the completeness of the opposition, 
it is not, however, required that the notion should 
be determined through every possible contradictory 
opposition ; for those at least ought to be omitted, 
concerning whose existence or non-existence the notion 
itself decides. In regard to the opposition itself, it 
is not required that the division should be carried 
through by contradictory oppositions. The only oppo- 
sition necessary is the reciprocal exclusion of the 
inferior notions into which the higher notion is 
divided." " In a mere logical relation, indeed, as we 
know nothing of the nature of a thing more than that 
a certain character either does or does not belong to 
it, a strictly logical division can only consist of two 
contradictory members, for example, — that angles are 
either right or not right, — that men are either white 
or not white. But looking to the real nature of the 
thing known, either a iwiori or a posteyioiH, the divi- 
sion may be not only dichotomous but polytomous, 
as for example, — angles are right, or acute, or obtuse ; 
men are white, or black, or copper-coloured, or olive- 
coloured, &c. 
Rules of We now come, in the second place, to the rules 
Divishra. dictated for Logical Division. 

These Rules spring either, 1°, From the Principle of 

o E«ser, Logil; § 136 Ed. 



LECTURES ON LOGIC. 31 

Division : or, 2°, From the Eelations of the Dividing lect. 

^ XXV. 



Members to the Divided Whole ; or, 3°, From the 
Eelations of the several Dividins; Members to each 
other ; or, 4°, From the relations of the Divisions to 
the Subdivisions. 

The first of these heads, — the Principle of Division, Those 
— comprehends the three first rules. Of these the l From^the 
first is self-evident, — There must be some principle, DivS! ° 
some reason, for every division ; for otherwise there ^"'^ ^''''^' 
would be no division determined, no division carried 
into efi'ect. 

In regard to the second rule, — That every division Second, 
should have only a single principle,' — the propriety of 
this is likewise sufficiently apparent. In every divi- 
sion we should depart from a definite thought, which 
has reference either to the notion as a unity, or to some 
single character. On the contrary, if we do not do 
this, but carry on the process by difi"erent principles, 
the series of notions in which the division is realised, 
is not orderly and homogeneous, but heterogeneous 
and perplexed. 

The third rule, — That the principle of division should Tiiird. 
be an actual and essential character of the divided 
notion, — is not less manifest. " As the ground of divi- 
sion is that w^hich principally regulates the correctness 
of the whole process, that is, the completeness and 
opposition of the division, — it follow^s that this ground 
must be of notoriety and importance, and accommo- 
dated to the end for the sake of which the division is 
instituted. Those characters of an object are best 
adapted for a division, whose owm determinations 
exert the greatest influence on the determinations of 
other characters, and, consequently, on those of the 
notion itself ; but such are manifestly not the external 



32 LECTURES ON LOGIC. 

LECT. and contino;ent, but tlie internal and essential, cha- 

X XV 

L racters, and, of these, those have the pre-eminence 

through whose determination the greater number of 
others are determined, or, what is the same thing, 
from which, as fundamental and original attributes, 
the greater number of the others are derived. The 
choice of character is, however, for the most part, regu- 
lated by some particular end ; so that, under certain 
circumstances, external and contingent characters may 
obtain a preponderant importance. Such ends cannot, 
however, be enumerated. The character affording the 
principle of division must likewise be capable of being 
clearly and definitely brought out ; for unless this be 
possible, we can have no distinct consciousness of the 
completeness and contrast of the determination of 
which it is susceptible. We ought, therefore, always 
to select those characters for principles of division, 
which are capable of a clear and distinct recogni- 
tion.'"' 

The second part of the rule, — That the division be 
not, therefore, too complex, and without a purpose, — is 
a corollary of the first. " In dividing, we may go on 
to infinity. For while, as was formerly shown, there 
is, in the series of higher and lower notions, no one 
which can be conceived as absolutely the low^est ; 
so in subdividing, there is no necessary limit to the 
process. In like manner, the co-ordinations may be 
extended ad infinitum. For it is impossible to exhaust 
all the possible relations of notions, and each of these 
may be employed as the principle of a new division. 
Thus we can divide men by relation to their age, to 
their sex, to their colour, to their stature, to their 
knowledge, to their riches, to their rank, to their man- 

o Esser, Loijik, § 137. — Ed. 



LECTURES ON LOGIC. 33 

ner of life, to their education, to their costume, &c. &c. lect. 

xxv. 
It would, however, be ridiculous, and render the divi 

sions wholly useless, if we multiplied them in this 
fashion without end. We, therefore, intentionally 
restrict them, that is, we make them comparatively 
limited, inasmuch as we only give them that complete- 
ness which is conducive to a certain end. In this 
manner divisions become relatively useful, or acquire 
the virtue of adaptation. In the selection of a prin- 
ciple of division, we must take heed whether it be 
fertile and pertinent. A ground of division is fertile, 
when it affords a division out of which again other 
important consequences may be drawn ; it is pertinent, 
when these consequences have a proximate relation to 
the end, on account of which we were originally in- 
duced to develop the extension of a concept. A prin- 
ciple of division may, therefore, be useful with one 
intent, and useless with another. Soldiers, for example, 
may be conveniently divided into cavalry and infantry, 
as this distinction has an important influence on their 
determination as soldiers. But in considerino; man in 
general and his relations, it would be ludicrous to 
divide men into foot and liorsemen ; while, on the 
contrary, their division would be here appropriate 
according to principles which in the former case would 
have been absurd. Seneca" says well, — 'Quicquid in 
majus crevit facilius agnoscitur, si discessit in partes ; 
quas innumerabiles esse et parvas non oportet. Idem 
euim vitii habet nimia, quod nulla divisio. Simile 
confuso est, quicquid usque in pulverem sectum est.'"^ 

Under the second head, that is, as springing from ii. From 
the relations of the Dividing Members to the Divided tionsVf the 
Wholes, there are included the fourth and fifth laws. Member^s to 

a Einst, 90. /3 Krug, Lorjik, § 126, Anm. 4.— Ed. 

VOL. II. C 



34) LECTURES ON LOGIC. 

LECT. " As the notion and the notions into which it is di- 
L_ vided, stand to each other in the relation of whole and 



the Divided 
Wholes. 



parts, and as the whole is greater than the part, the 
Fourth. fourth rule is manifestly necessary, viz. That no divid- 
ing member of the predicate must by itself exhaust 
the subject. When this occurs, the division is vicious, 
or, more properly, there is no division. Thus the 
division of raan into rational animals and unculti- 
vated nations, would be a violation of this law. 
Fifth. " On the other hand, as the notions into which a 

notion is divided, stand to each other in the relation of 
constituting parts to a constituted whole, and as the 
whole is only the sum of all the parts, the necessity 
of the fifth rule is manifest, — That the dividing mem- 
bers of the predicate, taken together, must exhaust the 
subject. For if this does not take place, then the 
division of the principal notion has been only partial 
and imperfect. We transgress this law, in the first 
place, when we leave out one or more members of divi- 
sion ; as for example, — The actions of men are either 
good or had, — for to these we should have added or 
indifferent. And in the second place, we transgress it 
when we co-ordinate a subdivision with a division ; as 
for example, — Philosophy is either theoretical ijhilo- 
sophy or moral p)hilosophy : here the proper opposition 
would have been theoretical philosophy and practical 
philosophy.""' On the other hand, the dividing mem- 
bers, taken together, must not do more than exhaust 
the subject. The definition of the whole must apply 
to every one of its parts, but this condition is not ful- 
filled if there be a dividing member too much, that is, 
if there be a notion brought as a dividing member, 
which, however, does not stand in subordination to 

a Esser, Logik, § 137.— Ed. 



LECTURES ON LOGIC. 35 

the divided whole. For example, — Mathematical fig- lect. 

ures are either solids or surfaces [or lines or points']. '— 

Here the two last members (lines and points) are re- 
dundant and erroneous, for lines and points, though 
the elements of mathematical figures, are not them- 
selves figures. 

Under the third head, as sprino;ino; from the rela- ni. From 

, the rela- 

tions of the several Dividing Members to Each Other, tions of the 

there is a sino^le law, the sixth, which enjoins, — That Dividing 

,,..,, . „ , . Members to 

the dividmg members be reciprocally exclusive. Each other. 

" As a division does not present the same but the dif- 
ferent determinations of a single notion, (for otherwise 
one and the same determination would be presented 
twice), the dividing members must be so constituted 
that they are not mutually coincident, so that they 
either in whole or in part contain each other. This 
law is violated when, in the first place, a subdivision 
is placed above a division, as, — Philosophy is either 
theoretical philosophy, or moral philosop)hy, or prac- 
tical philosophy; here moral philosophy falls into 
jyractical 2'>hilosophy as a subordinate part ; or when, 
in the second place, the same thing is divided in dif- 
ferent points of view, as, — Human actions are either 
necessary, or free, or useful, or detrimental.'"^ 

Under the fourth and last head, as arising from the iv. From 
relations of the Divisions to the Subdivisions, there is tions of the 
contained one law, the seventh, which prescribes, — the Sub- 
That the divisions proceed continuously from imme- seventh. 
diate to mediate difierences, {Divisio ne fiat per saltum 
vel hiatnm). 

" As divisions originate in the character of a notion, 
capable of an opposite determination, receiving this 
determination, and as the subdivisions originate in 

a Esser, Logik, § 137.— Ed. 



XXV. 



36 LECTUEES ON LOGIC. 

LECT. these opposite determinations being themselves again 
capable of opposite determinations, in which gradual 
descent we may proceed indefinitely onwards, — from 
this it is evident, that the divisions should, as far as 
possible, be continuous, that is, the notion must first 
be divided into its proximate, and then into its re- 
moter parts, and this without overleaping any one 
part ; or in other words, each part must be immedi- 
ately subordinated to its whole."" Thus, when some 
of the ancients divided philosophy into rational, and 
natural, and moved, the first and second members are 
merely subdivisions of theoretical philosophy, to which 
moral as j^i'ci'Ctical p>hilosophy is opposed. Sometimes, 
however, such a spring, — such a salt us, — is, for the sake 
of brevity, allowed ; but this only under the express 
condition, that the omitted members are interpolated 
in thought. Thus, many mathematicians say, angles 
are either right, or acute, or obtuse, although, if the 
division were continuous, — without hiatus, it would 
run, angles are either right or oblique; and the ob- 
lique, again, either acute or obtuse. 

a Esser, Lor/ik, § 1.37. — Ed. 



LECTURES ON LOGIC. 37 



LECTUEE XXVI. 
METHODOLOGY. 

SECTION TI. LOGICAL METHODOLOGY. 

III. — DOCTRINE OF PROBATION. 

We now proceed to the Third Part of Pure Meth- lect. 

XXVI 

odology, that which guides us to the third character 



or virtue of Perfect Thinking,— the Concatenation of ^'■°^""°"- 
Thought ; — I mean Probation, or the Leading of Proof. 
I commence with the following paragraph : — 

H LXXXVI. AVhen there are propositions or Par. lxxxvi. 
judgments which are not intuitively manifest, -itsNatiie 
and the truth of which is not admitted, thenments. 
their validity can only be established when we 
evolve it, as an inference, from one or more judg- 
ments or propositions. This is called Probation, 
Proving, or the Leading of Proof (prohatio, ar- 
gumentatio, or demonstratio in its wider sense). 
A Probation is thus a series of thoughts, in which 
a plurality of different judgments stand to each 
other, in respect of their validity, in the depend- 
ence of determining and determined, or of ante- 
cedents and consequents. In every Probation 
there are three things to be distinguished, — 
1°, The Judgment to be Proved, (thesis); 2°, The 



XXVI. 



88 LECTURES ON LOGIC. 

LECT. Ground or Principle of Proof, (argumentum) ; 

and, 3°, The Cogency of this principle to neces- 
sitate the connection of antecedents and conse- 
quents, {vis demonstrationis or nervus probandi). 
From the nature of Probation, it is evident that 
Probation without inference is impossible; and 
that the Thesis to be proved and the Principles 
of Proof stand to each other as conclusion and 
premises, with this difference, that, in Probation, 
there is a judgment (thesis) expressly supposed, 
which in the Syllogism is not, at least necessarily, 
the case." 



Expiica- In regard to the terms here employed, it is to be 
Terms em- noticcd that the term argumentation {argumentatio) 
Ar|umenta- Is applied uot ouly to a reasoning of many syllogisms, 
Argument, but likcwisc to a reasoning of one. The term argu- 
ment {argumentum), in like manner, is employed not 
only for the ground of a consecutive reasoning, but 
for the middle term of a single syllogism. But it is, 
moreover, vulgarly employed for the whole process of 
argumentation.^ 
Demonstra- The term demonstration {demonstratio) is used in a 
looser, and in a stricter, signification. In the former 
sense, it is equivalent to 'prohation, or argumenta- 
tion in general; in the latter, to necessary probation, 
or argumentation from intuitive principles. 
Leading of Thc cxpressiou leading of proof might, perhaps, be 
sorts. translated by the term deduction, but then this term 
must be of such a latitude as to include induction, to 
which it is commonly opposed; for Probation may be 

a Esser, Locjik, § 138. Cf. Krug, fang der Logik, § 32 et seq.'] 
Logik, § 127.— Ed. [Cf. Eichter, )3 See above, vol. i. p. 278.— Ed. 
JJher den Gegenstand und den Urn- 



LECTURES ON LOGIC. 39 

either a process of Deduction, that is, the leading of lect. 

proof out of one higher or more general proposition, 

or a process of Induction, that is, the leading of proof 
out of a plurality of lower or less general judgments. 

To prove, is to evince the truth of a proposition not Probation 
admitted to be true, from other propositions the truth 
of which is already established. In every probation 
there are three things to be distinguished : — l°,The Pro- 
position to be Proved, — the Thesis; 2°, The Grounds 
or Principle of Proof, — the Argument; and, 3°, The 
Degree of Cogency with which the thesis is inferred 
by the argumentum or argumenta, — the vis or nervus 
'prohandi. All probation is thus syllogistic; but all How disUu- 
syllogism is not probative. The peculiarity of proba- from Syiio- 
tion consists in this, — that it expressly supposes a^'"™' 
certain given proposition, a certain thesis, to be true ; 
to the establishment of this proposition the proof is 
relative; this proposition constitutes the conclusion 
of the syllogism or series of syllogisms of which the 
probation is made up : whereas, in the mere syllogistic 
process, this supposition is not necessarily involved. 
It is also evident that the logical value of a probation whereon 

, , o r\ -x ^ c • • ' ^ depends tlie 

depends, — 1 , (Jn the truth oi its principles or argu- logical value 
menta, 2°, On their connection with each other and tion. 
with the thesis or proposition to be proved, and, 3°, 
On the logical formality of the inference of the thesis 
from its argumenta. No proposition can be for an- 
other the principle of proof, which is not itself either 
immediately or mediately certain. A proposition is 
immediately certain, or evident at first hand, when, 
by the very nature of thought, we cannot but think 
it to be true, and when it, therefore, neither requires 
nor admits of proof. A proposition is mediately cer- 
tain, or evident at second hand, when it is not at 



40 LECTURES ON LOGIC. 

LECT. once and in itself thoiiglit as necessarily true, but 
•^^^^' when we are able to deduce it, with a consciousness 
of certainty, from a proposition which is evident 
at first hand. The former of these certainties is 
called self-evident, iyituitive, original, ijrimm^ij, ulti- 
mate, &c., and the latter, demonstrative, derivative, 
secondary, &c. 
Ground of Accordiug to this distinction, the Ground or Prin- 
Ab^oiuteor ciplc of Proof is either absolute or relative. Ab- 
solute, when it is an intuitive; relative, when it is 
a demonstrative, proposition. That every proposition 
must ultimately rest on some intuitive truth, — on some 
judgment at first hand, is manifest, if the fact of pro- 
bation itself be admitted; for otherwise the regress 
would extend to infinity, and all probation, conse- 
quently, be impossible. When, for example, in the 
series of grounds H, G, F, E, D, C, B, there is no ulti- 
mate or primary A, and when, consequently, every 
A is only relatively, in respect of the consequent 
series, but not absolutely and in itself, first; — in this 
case, no sufficient and satisfactory probation is pos- 
sible, for there always remains the question concern- 
ing a still higher principle. But positively to show 
that such primary judgments are actually given, is an 
exposition which, as purely metaphysical, lies beyond 
the sphere of Logic." 
Distinction To tho gcucral form of a system of Proof belong the 
tions*irre- followlug distinctious of propositions, to which I 
general form formerly alluded,^ and which I may again recall to 
of Proof!"" your remembrance. Propositions are either Tlieore- 
and Practi- tical ov Practical. Practical, when they enounce the 
way in which it is possible to effectuate or produce 

a Compare Esser, Logik, § 138. — j3 See above, vol. i. p. 265. — Ed. 
Ed. 



LECTURES ON LOGIC. 41 

something; Theoretical, when they simply enunciate lect. 

a truth, without respect to the way in which this may '- 

be realised or produced.'' 

A Theoretical proposition, if a primary or intuitive Axiom. 
principle, is styled an Axiom. Examples of this are 
given in the four Fundamental Laws of Logic, and in 
the mathematical commonnotions — Theivlioleisgreater 
than its part, — If equals he added to equals, the ivholes 
are equal, &c. A Practical proposition, if a primary or Postulate. 
intuitive principle, is styled a Postulate. Thus Geo- 
metry postulates the possibility of drawing lines, — of 
producing them ad iiifinitum, of describing circles, &c. 

A Theoretical proposition, if mediate and demon- Theorem. 
strable, is called a Theorem. This is laid down as a 
Thesis, — as a judgment to be proved, — and is proved 
from intuitive principles, theoretical and practical. 
A Practical proposition, if mediate and demonstrable, Problem, 
is called a Problem. In the probation, the Problem 
itself is first enounced ; it is then shown in the solu- 
tion how that which is required is to be done, — is 
to be effected; and, finally, in the proof, it is demon- 
strated that through this procedure the solution of 
the problem is obtained. For example, in the geo- 
metrical problem, — to describe an equilateral triangle 
on a given straight line; — there this problem is first 
stated; the solution then shows that, with this given 
line as a semi-diameter, we are to describe from each 
of its points of termination a circle ; the two circles 
will intersect each other, and we are then, from the 
point of intersection, to draw straight lines to each 
point of termination ; this being done, the proof 
finally demonstrates that these circles must intersect 
each other, that the drawn straight lines necessarily 

o [Fries, System der Logik, § 73.] 



42 LECTURES ON LOGIC. 

LECT. constitute a triangle, and that this triangle is neces- 
sarily equilateral. 



Corollaries. CoToUaries or Consectaries are propositions which, 
as flowing immediately as collateral result of others, 

Empeire- Tcquirc no separate proof. Emi^eiremata or Eiyipiri- 
cal Judgments are propositions, the validity of which 

Scholia, reposes upon observation and experience. Scholia or 
Comments are propositions which serve only for illus- 

Lemmata. tratiou. Lemmata or Sumjytions are propositions, bor- 
rowed either from a different part of the system we 
treat of, or from sciences other than that in which we 

Hypotheses. DOW cmploy tlicm. Finally, Hypotheses are proposi- 
tions of two different significations. For, in the first 
place, the name is sometimes given to the arbitrary 
assumption or choice of one out of various means of 
accomplishing an end ; when, for example, in the 
division of the periphery of the circle, we select the 
division into 360 degrees, or when, in Arithmetic, 
we select the decadic scheme of numeration. But, 
in the second place, the name of hypothesis is more 
emphatically given to provisory suppositions, which 
serve to explain the phenomena in so far as ob- 
served, but which are only asserted to be true, if 
ultimately confirmed by a complete induction. For 
example, the supposition of the Copernican solar sys- 
tem in Astronomy." 

Now these various kinds of propositions are mutu- 
ally concatenated into system by the Leading of Proof, 
— by Probation, 

So much for the character of this process in gen- 
eral. The paragraph, already dictated, contains a 
summary of the various particular characters by 
which Probations are distinguished. Before consid- 

a [Fries, System der Logik, § 73. Krug, Logik, §§ 67, G8.] 



LECTURES ON LOGIC. 43 

ering these in detail, I shall offer some preparatory lect. 
observations. 



" The differences of Probations are dependent The differ- 

ences of 

partly on their Matter, and partly on the Form in J^^^J""" 
which they are expressed. ErVauer 

" In respect of the former sfroimd of difference, — ami partly 

^ ^ . T-> ^"^ tlieir 

the Matter, — Probations are distinguished into Pure Form. 
or a priori and into Empirical or a posteriori, accord- of the'i?^^'^ 

„ , , . . I 1 • 1 , Matter,Pro- 

mg as they are lounded on principles wnicn we must bations are 

1 Pure and 

recognise as true, as constituting the necessary con- Empirical, 
ditions of all experience, or which we do recognise as 
true, as particular results given by certain applica- 
tions of experience. In respect of the latter ground 2. in re- 
of difference, — the Form, — Probations fall into various their Form. 
classes according to the difference of the form itself, 
which is either External or Internal. 

" In relation to the Internal Form, probations are »• Iq rela- 
tion to the 

divided into Direct or Ostensive and into Indirect or internal 

Form, 

Apagogical, according as they are draw^n from the Probations 
thine; itself or from its opposite, in other words, ac- or Ostensive 

Y . . . . . and Indirect 

cording as the principles of probation are positive or oy Apago- 
are negative." ° — Under the same relation of Internal synthetic or 
Form, they are also distinguished by reference to their 
order of procedure, — this order being either Essential 
or Accidental. The essential order of procedure re- 
gards the nature of the inference itself, as either from 
the whole to the part, or from the parts to the whole. 
The former constitutes Deductive Probation, the latter 
Inductive. The accidental order of procedure regards 
only our point of departure in considering a probation. 
If, commencing with the highest principle, we descend Progressive, 
step by step to the conclusion, the process is Synthe- tic or Re- 
tic or Progressive ; here the conclusion is evolved out ^'"'''*""'' 

o Esser, Loglk, § 141. — Ed. 



44 LECTURES ON LOGIC. 

LECT. of tlie principle. If again, starting from the conclu- 

L sion, we ascend step by step to the highest principle, 

the process is Analytic or Kegressive ; here the prin- 
ciple is evolved out of the conclusion, 
b. External In rcspcct to the External Form, Probations are 
Probations Simple or Monosyllogistic, if they consist of a single 

are Simple . ,. . -r> i it • • • n t • j_ 

and Com- rcasoning, Composite or rolysyllogistic it they consist 
Regukrand of ^ plurality of rcasoniugs. Under the same relation 
Perfect'^Ind of cxtemal form, they are also divided into Regular 
Imperfect. ^^^ Irrcgular, into Perfect and Imperfect. 
3. Accord- Another division of Probations is by reference to 
Degree of their Cogcncy, or the Degree of Certainty with which 
Probations thcir infcrencc is drawn. But their cogency is of 

areApodeic- . . ii**i t • ' i -it 

tic and various degrees, and this either objectively considered, 
that is, as determined by the conditions of the proof 
itself, or subjectively considered, that is, by reference 
to those on whom the proof is calculated to operate 
conviction. In the former or objective relation, pro- 
bations are partly Apodeictic, or Demonstrative in the 
stricter sense of that term, — when the certainty they 
necessitate is absolute and complete, that is, when the 
opposite alternative involves a contradiction ; partly 
Probable, — when they do not produce an invincible 
assurance, but when the evidence in favour of the 
conclusion preponderates over that which is opposed 

Universally to it. lu the latter or subjective relation, probations 

and Parti- . . "^ 

cuiariy arc citlier Universally Valid, when they are calculated 

Valid. . . ,, 1 1 • 1 -T~» 

to operate conviction on all reasonable mmds, or Par- 
ticularly Valid, when they are fitted to convince only 
certain individual minds. 



Par. Lxxxvii. H LXXXVII. Probations are divided by refer- 

Probations, i-Tiir i-t-i ii- 

-tbeir ence to their Matter, to their Form, and to their 

Divisions. 

Degree oi Cogency. 



LECTURES ON LOGIC. 45 

In relation to their Matter, they are partly lect. 
Pure or a priori, partly Empirical or a iwsie- — I — '. 
riori. 

As to their Form, — this is either Internal or 
External. In respect to their Internal Form, 
they are, 1°, By reference to the Manner of Infer- 
ence, Direct or Ostensive (SetAcrt/cat, ostensivce), 
and Indirect or Apagogical {jyrobationes apago- 
gicce, reductiones ad ahsiirdum) ; 2°, By refer- 
ence to their Essential or Internal Order of Pro- 
cedure, they are either Deductive or Inductive ; 
3°, By reference to their Accidental or Exter- 
nal Order of Procedure, they are partly Synthetic 
or Progressive, partly Analytic or Regressive. 
In respect to their External Form, they are, 
1°, Simple or Monosyllogistic, and Composite or 
Poly syllogistic ; 2°, Perfect and Imperfect ; 3°, 
Regidar and Irregular. 

In respect to their Degree of Cogency, they 
are, 1°, As objectively considered, either Apodeic- 
tic or Demonstrative in the stricter signification 
of the term, (aTroSei^ets, demonstrationes stricte 
dictce), or Probable, [probationes sensu latiori) ; 
2°, As subjectively considered, they are either 
Universally Valid, {Kar aky)6eCav, secundmn veri- 
tatem), or Particularly Valid {Kar avOpoiTrov, 
ad hominem)."' 



ica- 
tiou. 

ions, 
1. lu respect 



To speak now of these distinctions in detail. In the Expi 
first place, " Probations," we have said, " in relation to Probati 
their matter, are divided into Pure or cc p)riori, and of tbei 

• 1 -r\ • • ^ • • -r» • • Matter, are 

into Empirical or a posteriori. Pure or a j^non Pure and 

Empirical. 

a Cf. Krug, Lofjik, §§ 128, 129, —Ed. [Cf. Degeraiido, Des Sic/nes, 
130, 131, 132; Esser, Logik, § 139. t. iv. ch. 7, p. 234.] 



46 LECTURES ON LOGIC. 

LRCT. proofs are those that rest on principles which, although 

XXVI. . . . ^ • 1 • c 
rising into consciousness only on occasion or some 

external or internal observation, — of some act of expe- 
rience, are still native, are still original, contributions 
of tlie mind itself, and a contribution without which no 
act of experience becomes possible. Proofs again are 
called Empirical or a posteriori, if they rest on prin- 
ciples which are exclusively formed from experience 
or observation, and w^iose validity is cognisable in 
no other way than that of experience or observation. 
When the principles of Probation are such as are not 
contingently given by experience, but spontaneously 
engendered by the mind itself, these principles are 
always characterised by the qualities of necessity and 
universality; consequently, a proof supported by them 
is elevated altogether above the possibility of doubt. 
When, on the other hand, the principles of Probation 
are such as have only the guarantee of observation 
and experience for their truth, — (supposing even that 
the observation be correct and the experience stable 
and constant), — these principles, and, consequently, 
the probation founded on them, can pretend neither 
to necessity nor to universality ; seeing that what pro- 
duces the observation or experience, has only a rela- 
tion to individual objects, and is only competent to 
inform us of what now is, but not of what always is, 
of what necessarily must be. Although, however, 
these empirical principles are impressed with the cha- 
racter neither of necessity nor of universality, they 
play a very important part in the theatre of human 
Thisdistinc- thouo-ht.'"^ This distinction of Proofs, by reference 

tionofPro- ^ ... 

bationsnot to tlic matter of our knowledsje, is one, indeed, which 

taken into . . ^ 

account by Logic docs not take into account. Logic, in fact, con- 

Jjogic, '-' 

a Esser, Loyik, § 140. — Ed. 



LECTURES ON LOGIC. 47 

siclers every inference of a consequent from an antece- lect, 
dent as an inference a priori, supposing even that the — — '- 



antecedents themselves are only of an empirical cha- 
racter. Thus we may say, that, from the general rela- 
tions of distance found to hold between the planets, 
Kant and Olbers proved a priori that between Mars 
and Jupiter a planetary body must exist, before Ceres, 
Pallas, Juno, and Vesta were actually discovered.'^ 
Here, however, the a priori principle is in reality only 
an empirical rule, — only a generalisation from expe- 
rience. But with the manner in which these em- 
pirical rules (Bacon would call them axioms) are 
themselves discovered or evolved, — with this Pure 
Logic has no concern. This will fall to be considered 
in Modified Logic, when we treat of the concrete 
Doctrine of Induction and Analogy. 

In the second place, "in respect of their Form, and 2. in respect 
that the Internal, Probations are, as we said, first of Form,— 
all, divided into Direct or Ostensive, and into Indirect and ia-*^ 
or Apagogical. A proof is Direct or Ostensive, when '"^'''" 
it evinces the truth of a thesis through positive princi- 
ples, that is, immediately ; it is Indirect or Apagogical, 
when it evinces the truth of a thesis through the false- 
hood of its opposite, that is, mediately. The indirect 
is specially called the cqxtgogical, (argumentatio apa- 
gogica sive deductio ad impossibile), because it shows 
that something cannot be admitted, since, if admitted, 
consequences would necessarily follow impossible or 
absurd. The Indirect or Apagogical mode of proof is Principle 
established on the principle, that that must be con- Proof.'"'' 
ceded to be true whose contradictory opposite con- 
tains within itself a contradiction. This principle 

a See Kaut's Vorlesungen ilher vi. p. 449. — Ed. 
Phijsische Geographk, 1802 ; Werke, 



48 LECTURES ON LOGIC. 

LECT. manifestly rests on the Law of Contradiction and on 

L the Law of Excluded Middle ; for what involves a 

contradiction it is impossible for us to think, and if a 
character must be denied of an object, — and that it 
must be so denied the probation has to show, — then 
the contradictory opposite of that character is of 
necessity to be affirmed of that object. The Direct 
mode of probation has undoubtedly this advantage 
over the Indirect, — that it not only furnishes the 
sought-for truth, but also clearly develops its neces- 
sary connection with its ultimate principles ; whereas 
the Indirect demonstrates only the rupugnance of some 
proposition with certain truths, without, however, 
positively evincing the truth of its opposite, and 
thereby obtaining for it a full and satisfactory recog- 
nition. It is, therefore, usually employed only to 
constrain a troublesome opponent to silence, by a 
display of the absurdities which are implied in, and 
which would flow out of, his assertions. Nevertheless 
the indirect probation establishes the proposition to 
be proved not less certainly than the direct ; nay, it 
still more precisely excludes the supposition of the 
opposite alternative, and, consequently, affords an 
intenser consciousness of necessity. We ought, how- 
ever, to be on our guard against the paralogisms to 
which it is peculiarly exposed, by taking care — 1°, 
That the opposites are contradictory and not con- 
trary ; and, 2°, That an absurdity really is, and not 
Differences mcrcly appcars to be. The differences of Apagogical 
or Apagogi- Probatlous correspond to the different kinds of propo- 

cal Proba- 

tions. sitions which may be indirectly demonstrated ; and 
these are, in their widest generality, either Categori- 
cal, or Hypothetical, or Disjunctive. Is the thesis a 
categorical proposition 1 Its contradictory opposite is 



LECTUEES ON LOGIC. 49 

sions are deduced, until we obtain one of so absurd a lect. 
character, that we are able to argue back to the false- — ^ 1 



hood of the original proposition itself. Again, is the 
thesis an hypothetical judgment 1 The contradictory- 
opposite of the consequent is assumed, and the same 
process to the same end is performed as in the case of 
a categorical proposition. Finally, is the thesis a dis- 
junctive proposition ? In that case, if its memhra 
disjuncta are contradictorily opposed, we cannot, either 
directly or indirectly, prove it false as a whole ; all that 
we can do being to show that one of these disjunct 
members cannot be affirmed of the subject, from which 
it necessarily follows that the other must." " 

Under the Internal Form, Probations are, in the ^ Deduc- 
tive and 

second place, in respect of their Essential or Internal inductive. 
Order of procedure, eitlier Deductive or Inductive, 
according as the thesis is proved by a process of rea- 
soning descending from generals to particulars and 
individuals, or by a process of reasoning ascending 
from individuals and particulars to generals. On this 
subject it is not necessary to say anything, as the 
rules which govern the formal inference in these pro- 
cesses have been already stated in the Doctrine of 
Syllogisms ; and the consideration of Induction, as 
modified by the general conditions of the matter to 
which it is applied, can only be treated of when, in 
the sequel, we come to Modified or Concrete Method- 
ology. 

" Under the Internal Form, Probations are, how- c sj-ntuetic 

ii'ii • r»i'Ti 1 ^^'^ Analy- 

ever, m the third place, m respect of their h/xternal tic. 
or Accidental Order of procedure. Synthetic or Pro- 
gressive, and Analytic or Regressive. A probation 

a Esser, Lo<jilc, § 142.— Ed. 
VOL. IL D 



50 LECTUKES ON LOGIC. 

LECT. is called synthetic or 2^i^og7'ess{ve, when the conclusion 
-^ — - is evolved out of the principles, — analytic or regressive 
when the principles are evolved out of the conclusion. 
In the former case, the probation goes from the sub- 
ject to the predicate ; in the latter case, from the 
predicate to the subject. Where the probation is com- 
plex, — if synthetic, the conclusion of the preceding syl- 
logism is the subsumption of that following ; if analy- 
tic, the conclusion of the preceding syllogism is the 
sumption of that following. In respect of certainty, 
both procedures are equal, and each has its peculiar 
advantages ; in consequence of which the combination 
of these two modes of proof is highly expedient. But 
the Analytic Procedure is often competent where 
the Synthetic is not ; Avhereas the Synthetic is never 
possible where the Analytic is not, and this is 
never possible where we have not a requisite stock of 
propositions already verified. When the Probation is 
partly analytic, partly synthetic, it is called Mixed.""' 

P-;L^xxxviii. ^ LXXXVIII. The Formal Legitimacy of a 
Legitimacy Probatlou Is determined by the foUowinp; rules. 

01 a Proba- -^ ^ 

tion,— its 1 ° Nothin o; is to be beofo-ed, borrowed, or stolen ; 

that is, nothing is to be presupposed as proved, 
which itself requires a demonstration. The vio- 
lation of this rule affords the vice called the 
Petitio jyi'incijyii, or Fallacia qucesiti niedii {to Iv 
a-f>yr\ alTelcrOai).^ 

2°, No proposition is to be employed as a prin- 
ciple of proof, the truth of which is only to be 

o Esser, Logil; § 142. — Ed. tV ttj apxji, id est, in principio; sed 

jS [On error of this term, see tov iv apxy TrpoKfi/ufvov, id est, ejus 

Pacius, Commentarius in Org. {In problematis, quod initio fuit proposi- 

Anal. Prior ii. 16. " Non est pe- turn et in disquisitionem vocatum." 

titio rfjs apxhs, id est, principii, vel Ibid, ii. 24. — Ed.] 



LECTURES ON LOGIC. 51 

evinced as a consequence of tlie proposition lect. 

which it is employed to prove. The violation of — L. 

this rule is the vice called varepov irpoTepov. 

3°, No circular probation is to be made ; that 
is, the proposition which we propose to prove 
must not be used as a principle for its own pro- 
bation. The violation of this rule is called the 
Orhis vel circulus in demonstrando, — dicdlelus, — 
6 oC aWrjkoiv rpoTTO?." 

4°, No leap, no hiatus, must be made ; that is, 
the syllogisms of which the probation is made up, 
must stand in immediate or continuous connec- 
tion. From the transgression of this rule results 
the vice called the Saltiis vel Hiatus in demon- 
strando. 

5°, The scope of the probation is not to be 
changed ; that is, nothing is to be proved other 
than what it was proposed to prove. The violation 
of this rule gives the Hetey^ozelesis, Ignoratio vel 
Mutatio elenchi, and the Transitus in aluid 
genus vel a genere ad genus, — /xera^Sao-is ets aWo 

In this paragraph, I have mven, as different rules, These mies 

, . , reduced to 

those canons which are opposed to vices not abso-two. 
lutely identical, and which have obtained different 
denominations. But you must observe, that the first 
three rules are all manifestly only various modifications 
— only special cases, — of one general law. To this law, 
likewise, the fourth rule may with perfect propriety 
be reduced, for the saltvs or Jiiatus in prohando is, in 

a See Sextus Empiricus, Pyrrh. ;8 [See Reinhold, Die Lorjilc odcr die 

Hyp.,!. 169, ii. 68. Laertius, L. ix. allgemcine JJenl-forinenlehre, % 150, p. 

§§ 88, 89. [Cf. Facciolati, Acroasis, 407, Jena, 1827.] [Cf. Krug, Lorjih, 

V. p. 69 ct scq.] § 133. Esser, Locjih, § 144.— Ed.] 



52 



LECTURES ON LOGIC. 



LECT. 
XXVI. 



Par.LXXXIX. 

Rules of 
Probation 
reduced to 
two. 



fact, no less the assumption of a proposition as a prin- 
ciple of probation which itself requires proof, than 
either the petitio principi% the hysteron protei^on, or 
the circulus in j)rohando. These five laws, therefore, 
and the correspondent vices, may all be reduced to 
two ; the one of which regards the means, — the 
principles of proof; the other the end, — the propo- 
sition to be proved. The former of these laws pre- 
scribes, — That no proposition be employed as a prin- 
ciple of probation, which stands itself in want of 
proof ; the latter, — That nothing else be proved than 
the proposition for whose proof the probation was in- 
stituted. You may, therefore, add to the last para- 
graph the following supplement : — 

IT LXXXIX. These rules of the logicians may, 
however, all be reduced to two. 

1°, That no proposition be employed as a Prin- 
ciple of Probation, which stands itself in need of 
proof 

2°, That nothing else be proved than the Pro- 
position for whose proof the Probation was in- 
stituted. 



Explica- 
tion. 



First Rule. 



Of these two, the former comprehends the first four 
rules of the logicians, — the latter the fifth. I shall 
now, therefore, proceed to illustrate the five rules in 
detail. 

The First Rule — Nothing is to be begged, borrowed, 
or stolen ; that is, nothing is to be presupposed as 
proved, which itself requires a demonstration,- — is, in 
fact, an enunciation of the first general rule I gave 
you, and to this, therefore, as we shall see, the second, 
third, and fourth are to be reduced as special appli- 



LECTURES ON LOGIC. 53 

cations. But, in considering this law In its univer- lect. 

. . XXVI 

sality, it is not to be understood as if every probation — 1 — L 
were at once to be rejected as worthless, in which un£^i!lch 
anything is presupposed and not proved. Were this Jo'be^,^der- 
its sense, it would be necessary in every probation to ^**""^' 
ascend to the highest principles of human knowledge, 
and these themselves, as immediate and, consequently, 
incapable of proof, might be rejected as unproved 
assumptions. Were this the meaning of the law, 
there could be no probation whatever. But it is not 
to be understood in this extreme rigour. That pro- 
bation alone is a violation of this law, and, conse- 
quently, alone is vicious, in which a proposition is 
assumed as a principle of proof, which may be doubted 
on the ground on which the thesis itself is doubted, 
and where, therefore, we prove the uncertain by the 
equally uncertain. The probation must, therefore, 
depart from such principles as are either immediately 
given as ultimate, or mediately admit of a proof from 
other sources than the proposition itself in question. 
When, for example, it was argued that the Newtonian 
theory is false, which holds colours to be the result 
of a diversity of parts in light, on the ground, ad- 
mitted by the ancients, that the celestial bodies, and, 
consequently, their emanations, consist of homoge- 
neous elements ; — this reasoning was inept, for the 
principle of proof was not admitted by modern 
philosophers. Thus, when Aristotle defends the in- 
stitution of slavery as a natural law, on the ground 
that the barbarians, as of inferior intellects, are the 
born bondsmen of the Greeks, and the Greeks, as of 
superior intellect, the born masters of the barbarians," 

o Polit., i. 2.— Ed. 



54 LECTURES ON LOGIC. 

•LECT. — (an argument which has, likeAvise, been employed 

in modern times in the British Parliament, with the 

substitution of negroes for barbarians, and whites 
for Greeks), — this argument is invalid, as assuming 
what is not admitted by the opponents of slavery. 
It would be a petitio principii to prove to the Mo- 
hammedan the divinity of Christ from texts in the 
New Testament, for he does not admit the authority 
of the Bible ; but it would be a valid argumentum 
ad hominem to prove to him from the Koran the pro- 
phetic mission of Jesus, for the authority of the Koran 
he acknowledges. 
Second The Second Eule, That no proposition is to be em- 

ployed as a principle of proof, the truth of which is 
only to be evinced as a consequence of the proposi- 
tion which it is employed to prove, — is only a special 
case of the preceding. For example, if we were to 
argue that man is a free agent, on the ground that 
he is morally responsible for his actions, or that his 
actions can be imputed to him, or on the ground 
that vice and virtue are absolutely different, — in these 
cases, the hysteron p)roteron is committed ; for only 
on the ground that the human will is free, can man 
be viewed as a morally responsible agent, and his ac- 
tions be imputed to him, or can the discrimination of 
vice and virtue, as more than a merely accidental rela- 
tion, be maintained. But we must pause before we 
reject a reasoning on the ground of hysteron proteron; 
for the reasoning may still be valid, though this logi- 
cal fault be committed. Nay, it is frequently neces- 
sary for us to reason by such a regress. In the very 
example given, if we be unable to prove directly that 
the will of man is free, but are able to prove that he 
is a moral agent, responsible for his actions, as sub- 



LECTURES ON LOGIC. 55 

jectecl to tlie voluutaiy but unconditioned Law of lect. 
Duty, and if the fact of this law of duty and its uu- — "- — L 
qualified obligation involve, as a postulate, an eman- 
cipation from necessity, — in that case, no competent 
objection can be taken to this process of reasoning. 
This, in fact, is Kant's argument. From what he calls 
the categorical imi^erative, that is, from the fact of 
the unconditioned law of duty as obligatory on man, 
he postulates, as conditions, the liberty of the human 
will, and the existence of a God, as the moral gover- 
nor of a moral universe.* 

The Third Law,^ — That no circular probation is to Third Rule, 
be made, that is, the proposition which we propose to 
23rove must not be used as a principle for its own pro- 
bation, — this, in like manner, is only a particular case 
of the first. " To the Circle there are required properly 
two probations, which are so reciprocally related that 
the antecedent in the one is proved by its own conse- 
quent in the other. The proposition A is true be- 
cause the proposition B is true ; and the proposition 
B is true because the proposition A is true. A circle 
so palpable as this would indeed be committed by no 
one. The vice is usually concealed by the interpola- 
tion of intermediate propositions, or by a change in 
the expression."'^ Thus Plato, in his Phcedo^ demon- 
strates the immortality of the soid from its simplicity ; 
and, in the Republic,^ he demonstrates its simplicity 
from its immortality. 

In relation to the Ilysteron Proteron and the Circle, Regressive 
I must observe that these present some peculiar diffi- gressive 

. o ^ Proofs not 

culties for the systematic arrangement oi our know- to be con- 

a Kritih der veinen Yernunft, Me- j3 Krug, Loijil; § 133. Anm. 3. — 

thodenlehre, Hauptst., ii. Abschn., 2. Ed. 
Kritik der praktischen Vernunft, p. y P. 78. — Ed. 
274, ed. Rosenkranz.— Ed. S B. x. p. 611.— Ed. 



56 LECTURES ON LOGIC. 

LEOT. ledo-e. Throu2;li the Circle, (the result of which is only 
the proof of an assertion), — through the circle by itself, 



finin.ici nothino- whatever is gained for the logical develop- 

with tlio O c^ <zj ■*• 

Scic"^''''^ ment of our knowledge. But we must take care not 
to confound the connection of Regressive and Pro- 
gressive Proofs with the tautological Circle. AVhen, 
in the treatment of a science out of the observed 
facts, we wish to generalise universal laws, we lead, 
in the first place, an inductive probation, that (ort) 
certain laws there are. Having assured ourselves of 
the existence of these laws by this regressive process, 
we then place them in theory at the head of a pro- 
gressive or synthetic probation, in which the facts 
again recur, reversed and illustrated from the laws, 
which, in the antecedent process, they had been em- 
ployed to establish ; that is, it is now shown why 
(Stort) these facts exist. 
Fourth The Fourth Rule, — No leap, no gap, must be made, 
that is, the syllogisms of which the probation is made 
up must stand in immediate or continuous connection, 
• — may be, likewise, reduced to the first. For here 
the only vice is that, by an ellipsis of an intermediate 
link in the syllogistic chain, we use a proposition which 
is actually without its proof, and it is only because 
this proposition is as yet unproved, that its employ- 
ment is illegitimate. The Saltus is, therefore, only a 
special case of the Petitio. 
The Saltus The Soltus is committed when the middle term of 
'siraudu.'' one of the syllogisms in a probation is not stated. 
If the middle term be too manifest to require state- 
ment, then is the saltus not to be blamed, for it is 
committed only in the expression and not in the 
thought. If the middle term be not easy of dis- 
covery, then the saltus is a fault ; but if there be 



LECTURES ON LOGIC. 57 

no middle term to be found, then the scdtus is a vice lect, 

which invalidates the whole remainder of the proba- L 

tion. The proper saltus, — the real violation of this 
law, is, therefore, when we make a transition from one 
proposition to another, the two not being connected 
together as reason and consequent." The (vulgar) 
Enthymeme and the Sorites do not, therefore, it is 
evident, involve violations of this law. 

The Fifth Eule, — The scope of the probation is not Fifth Rule, 
to be changed, that is, nothing is to be proved other 
than what was proposed to be proved, — corresponds 
to the second of the two rules which I gave, and of 
which it is only a less explicit statement. It evidently Admits of 
admits of three kinds or degrees. In the first case, grees. 
the proposition to be proved is changed by the 
change of its subject or predicate into different no- 
tions. Again, the proposition may substantially re- 
main the same, but may be changed into one either of 
a wider or of a narrower extension, — the second and 
third cases. 

The first of these cases is the Mutatio Elenchi, or First 
Transitus ad aliud genus, properly so called. " When Mltatlo 
a probation does not demonstrate what it ought to^^^"^*"'"* 
demonstrate, it may, if considered absolutely or in 
itself, be valid ; but if considered relatively to the pro- 
position which it behoves us to prove, it is of no value. 
We commute by this procedure the whole scope or pur- 
port of the probation ; we desert the proper object of 
inquiry, — the point in question. If a person would 
prove the existence of ghosts, and to this end prove 
by witness the fact of unusual noises and appear- 
ances during the night, he would prove something 
very dijfferent from what he proposed to establish ; 

a Of. Krug, Logik, § 133. Anm. 4.— Ed. 



58 LECTURES ON LOGIC. 



LECT. for this Avoiild be admitted without difficulty hj those 



XXVI 



who still denied the apparition of ghosts : it, therefore, 
behoved him to show that the unusual phoenomena 
were those of a spirit good or bad." " 
Second Dc- The two other cases, — when the proposition actually 
whk'rto''o proved is either of a smaller or of a greater extension 
proved than the proposition which ought to have been proved, 
— are not necessarily, like the preceding, altogether 
irrelevant. They are, however, compared together, of 
various degrees of relevancy. In the former case, 
where too little is proved, — here the end proposed is, 
to a certain extent at least, changed, and the proba- 
tion results in somethino; different from what it was 
intended to accomplish. For example, if we propose 
to prove that Sempronius is a virtuous character, 
and only prove the legality of his actions, we here 
prove something less than, something different from, 
what we professed to do ; for we proposed to prove 
the internal morality, and not merely the external law- 
fulness, of his conduct. Such a proof is not absolutely 
invalid ; it is not even relatively null, for the exter- 
nal legality is ahvays a concomitant of internal mor- 
ality. But the existence of the latter is not evinced 
by that of the former, for Sempronius may conform 
his actions to the law from expediency and not from 
duty.^ 
Third De- 111 the other case, in which there is proved too much, 
ihfciTtoo the probation is lawful, and only not adequate and 
proved.' precise. For example, if we propose to prove that the 
soul does not perish with the body, and actually prove 
that its dissolution is absolutely impossible, — here 
the proof is only superabundant. The logical rule, — 

o Krug, Loc/ik, % 133. Anm. 2.— ;3 Cf. Krug, Lor/ik, § 133. Anm. 5. 
Ed. —Ed. 



LECTURES ON LOGIC. 59 

Qui nimium 2')'i'ohat, nihil probat, is, therefore, in its lect. 
universal or unqualified expression, incorrect. The — ^ — '- 
proving too much is, however, often the sign of a 
saltus having been committed. For example, — when 
a religious enthusiast argues from the strength of his 
persuasion, that he is, therefore, actuated by the Holy 
Spirit, and his views of religion consequently true, — 
there is here too much proved, for there is implied 
the antecedent, omitted by a saltus, that whoever is 
strongly persuaded of his inspiration is really inspired, 
— a proposition too manifestly absurd to bear an ex- 
plicit enouncement. In this case, the apparent too 
much is in reality a too much which, when closely 
examined, resolves itself into a nothing." 

We have thus terminated the consideration of Pure 
or Abstract Logic, in both its Parts, and now enter on 
the Doctrine of Modified or Concrete Logic. 

a [Cf. Sigwart, Ilandbuch zu Vorksungen iiher die Logik, § 407, p. 252.] 



60 LECTURES ON LOGIC. 



LECTURE XXVII. 

MODIFIED LOGIC. 

PART I. — MODIFIED STOICHEIOLOGY. 

SECTION I. — DOCTRINE OF TRUTH AND ERROR. 

TRUTH. ITS CHARACTER AND KINDS. 

LECT. Having now terminated tlie Doctrine of Pure or Ab- 

'- stract Logic, we proceed to that of Modified or Con- 

Logtc!— Crete Logic. In entering on this subject, I have to 
Its object. j,QQ^ii ^Q jQ^^Y memory what has formerly been stated 
in regard to the object which Modified Logic pro- 
poses for consideration. Pure Logic takes into ac- 
count only tlie necessary conditions of thought, as 
founded on the nature of the thinking process itself. 
Modified Logic, on the contrary, considers the condi- 
tions to which thought is subject, arising from the 
empirical circumstances, external and internal, under 
which exclusively it is the will of our Creator that 
man should manifest his faculty of thinking. Pure 
Logic is thus exclusively conversant with the form ; 
Modified Logic is, likewise, occupied with the matter, 
of thought. And as their objects are difterent, so, 
likewise, must be their ends. The end of Pure Logic 
is formal truth, — the harmony of thought with 
thought ; the end of Modified Logic is the harmony 
of thought with existence. Of these ends, that which 
Pure Logic proposes is less ambitious, but it is fully 
and certainly accomplished ; the end which Modified 



LECTURES ON LOGIC. Gl 

Logic proposes is higher, but it is far less perfectly lect! 
attained. The problems which Modified Logic has to ' ^ 



solve may be reduced to three: 1°, What is Truth Lmslie- 
and its contradictory opposite, — Error ? 2°, What fhree'I *" 
are the Causes of Error and the Lnpediments to Truth, 
by which man is beset in the employment of his facul- 
ties, and what are the Means of their Removal ? And, 
3°, What are the Subsidiaries by which Human 
Thought may be strengthened and guided in the 
exercise of its functions 1 

From this statement it is evident that Concrete And distri- 
Loo;ic miolit, like Pure Lome, have been divided into tween its 
a Stoicheioloey and a Metliodolosy, — the former com- lo^v and its 
prismg the tirst two heads, — the latter the third, r or oiogy. 
if to Modified Stoicheiology we refer the considera- 
tion of the nature of concrete truth and error, and of 
the conditions of a merely not erroneous employment 
of thought, — this will be exhausted in the First and 
Second Chapters ; whereas if we refer to Methodology 
a consideration of the means of employing thought 
not merely without error but with a certain positive 
perfection, — this is what the Third Chapter professes 
to expound. 

I commence the First Chapter, which proposes to 
answer the question, — What is Truth 'i with its cor- 
relatives, — by the dictation of the following paragraj)h. 

H XC. The end which all our scientific efi'orts Par. xc. 
are exerted to accomplish, is Truth and Cer- Certainty, 

m 1 • 1 1 — what. 

tamty. Irutn is the correspondence or agree- 
ment of a cognition with its object ; its Criterion 
is the necessity determined by the laws which 
govern our faculties of knowledge ; and Certainty 
is the consciousness of this necessity." Certainty, 

o Cf. Twesten, I>ie Lofjik, inhe.ondcre die Analyiik, § 306. — Ed. 



62 LECTURES ON LOGIC. 

LECT, or the conscious necessity of knowledge, abso- 

'- lutely excludes the admission of any opj)osite 

supposition. Where such appears admissible, 
doubt and uncertainty arise. If we consider 
truth by relation to the degree and kind of Cer- 
tainty, we have to distinguish Knowledge, Belief, 
and Oimiion. Knowledge and Belief differ not 
only in degree but in kind. Knowledge is a 
certainty founded upon insight ; Belief is a cer- 
tainty founded upon feeling. The one is per- 
spicuous and objective ; the other is obscure and 
subjective. Each, however, supposes the other ; 
and an assurance is said to be a knowledge or 
a belief, according as the one element or the other 
preponderates. Opinion is the admission of 
something as true, where, however, neither in- 
sight nor feeling is so intense as to necessitate a 
perfect certainty. What prevents the admission 
of a proposition as certain is called Doubt. The 
approximation of the imperfect certainty of 
opinion to the perfect certainty of knowledge or 
belief is called Prohahility, 

If we consider Truth with reference to Know- 
ledge, and to the way in which this knowledge 
arises, we must distinguish Empirical or a 'pos- 
teriori, from Pure or a ^^riori Truth. The former 
has reference to cognitions which have their 
source in the presentations of Perception, Ex- 
ternal and Internal, and which obtain their form 
by the elaboration of the Understanding or Fa- 
culty of Relations [hidvoia.) The latter is con- 
tained in the necessary and universal cognitions 
afforded by the Regulative Faculty, — Intellect 
Proper, — or Common Sense, (voOs.) 



LECTURES ON LOGIC. G3 

This paragrapli, after stating that Truth and Cer- lect. 
tainty constitute the end of all our endeavours after 



knowledge, for only in the attainment of truth and ^^l]"^^' 
certainty can we possibly attain to knowledge or 
science ; — I say, after the statement of this manifest 
proposition, — it proceeds to define what is meant by 
the two terms Ti'utli and Certainty ; and, to com- 
mence with the former, — Truth is defined, the corre- 
spondence or agreement of a cognition or cognitive act 
of thought with its object. 

The question — What is Truth 1 is an old and cele- Truth,— 
brated problem. It was proposed by the Roman 
Governor, — by Pontius Pilate, — to our Saviour ; and it 
is a question which still recurs, and is still keenly agi- 
tated in the most recent schools of Philosophy. In one Definition 

. ^ ^ _ . of the term, 

respect, all are nearly agreed m regard to the deiini- 
tion of the term, for all admit that by truth is under- 
stood a harmony, — an agreement, — a correspondence 
between our thought and that which we think about. 
This definition of truth we owe to the schoolmen. 
" Veritas intellectus," says Aquinas, "est adcequatio in- 
tellectus et rei, secundum quod intellectus elicit esse, 
quod est, vel non esse, quod non est." " From the 
schoolmen, this definition had been handed down to 
modern philosophers, by whom it is currently em- 
ployed, without, in general, a suspicion of its origin. 
It is not, therefore, in regard to the meaning of the 
term truth, that there is any difi'erence of opinion 
among philosophers. The questions which have pro- Questions 
voked discussion, and which remain, as heretofore, regarding 
without a definitive solution, are not whether truth be 

a [Contra Gentiles, lib. i.e. 59. See Ruiz, Comment, de Scicntia, de Ideis, 
Biunde, t/ber Wahrlieit in Erhennen, de Veritate, &c. Disp. Ixxxv., p. 871 
p. 11. On Truth in general, see et seq.] 



64! LECTUKES ON LOGIC. 

LECT. tlie harmony of thought and reality, but whether this 
L harmony, or truth, be attainable, and whether we pos- 
sess any criterion by which we can be assured of its 
attainment. Considering, however, at present only the 
meaning of the term, philosophers have divided Truth, 
(or the harmony of thought audits object), into differ- 
ent species, to which they have given diverse names ; 
but they are at one, neither in the division nor in the 
nomenclature. 
For man It is plain that for man there can only be conceived 
kiwis of two kinds of Truth, because there are for human thousrht 

Trutli,— . . . ^ 

Formal and Quly two spcclcs of objcct. For that about which we 
think, must either be a thought, or something which a 
thought contains. On this is founded the distinction 
of Formal Knowledge and Real Knowledge, — of For- 
mal Truth and Real Truth. Of these in their order. 

I. Formal I. lu regard to the former, a thouo;ht abstracted 
from what it contains, that is, from its matter or what 
it is conversant about, is the mere form of thought. 
The knowledge of the form of thought is a formal 
knowledge, and the harmony of thought with the form 

Formal of thought is, conscquently. Formal Truth. No w Formal 

Truth of . . 

two kinds, Knowled2:e is of two kinds : for it reo;ards either the 

—Logical T . /. 1 . 

andMathe- couditious of tlic Elaborativc Faculty, — the Faculty 

matical. r>rni tt^ t- t-w 

of Thought Proper, — or the conditions of our Presen- 
tations or Representations of external things, that is, 
the intuitions of Space and Time. The former of these 
sciences is Pure Logic, — the science which considers 
the laws to which the Understanding is astricted in its 
elaborative operations, without inquiring what is the 
object, — what is the matter, to which tliese operations 
are applied. The latter of these sciences is Mathema- 
tics, or the science of Quantity, which considers the re- 
lations of Time and Space, without inquiring whether 



LECTURES ON LOGIC. 65 

there be any actual reality in space or time. Formal lect. 

. . XXVII 

truth will, therefore, be of two kinds, — Logical and — '- 



Mathematical. Logical truth is the harmony or agree- Logical 
ment of our thoughts with themselves as thoughts, in 
other words, the correspondence of thought with the 
universal laws of thinking. These laws are the object 
of Pure or General Logic, and in these it places the cri- 
terion of truth. This criterion is, however, only the nega- 
tive condition — only the conditio sine qua non, of truth. 
Logical truth is supposed in supposing the possibility 
of thought ; for all thought presents a combination, the 
elements of which are repugnant or congruent, but 
which cannot be repugnant and congruent at the same 
time. Logic might be true, although we possessed no 
truth beyond its fundamental laws ; although we knew 
nothing of any real existence beyond the formal hypo- 
thesis of its possibility. 

But were the I-iaws of Logic purely subjective, that 
is, were they true only for our thought alone, and 
without any objective validity, all human sciences, 
(and Mathematics among the rest), Avould be purely 
subjective likewise ; for we are cognisant of objects 
only under the forms and rules of which Logic is the 
scientific development. If the true character of ob- 
jective validity be universality, the laws of Logic are 
really of that character, for these laws constrain us, 
by their own authority, to regard them as the univer- 
sal laws not only of human thought, but of universal 
reason. 

The case is the same with the other formal science, Mathemati 
the science of Quantity, or Mathematics. Without ^^'^ 
inquiring into the reality of existences, and without 
borrowing from or attributing to them anything, 
Arithmetic, the science of Discrete Quantity, creates 

VOL. II. E 



QQ LECTURES ON LOGIC. 



LECT. its numbers, and Geometry, the science of Continuous 

XWII 

— '- Quantity, creates its figures ; and botli operate upon 

these their objects in absolute independence of all 
external actuality. The two mathematical sciences 
are dependent for their several objects only on the 
notion of time and the notion of space, — notions under 
which alone matter can be conceived as possible, for 
all matter supposes space, and all matter is moved in 
space and in time. But to the notions of space and time 
the existence or non-existence of matter is indifferent ; 
indifferent, consequently, to Geometry and Arithmetic, 
so long at least as they remain in the lofty regions of 
pure speculation, and do not descend to the practical 
application of their principles. If matter had no exist- 
ence, nay, if space and time existed only in our minds, 
mathematics would still be true ; but their truth would 
be of a purely formal and ideal character, — would fur- 
nish us with no knowledge of objective realities." 

So much for Formal Truth, under its two species of 
Logical and Mathematical 
Trut?'^^ The other genus of truth, — (the end which the Real 
Sciences propose), — is the harmony between a thought 
Real and aud its matter. The Real Sciences are those which 
Sciences, liavG a determinate reality for their object, and which 
are conversant about existences other than the forms 
of thought. The Formal Sciences have a superior 
certainty to the real ; for they are simply ideal com- 
binations, and they construct their objects without 
inquiring about their objective reality. The real sci- 
ences are sciences of fact, for the point from which 
they depart is always a fact, — always a presentation. 
Some of these rest on the presentations of Self-con- 

o Cf. E8ser, Lof/ik, § 172.— Ed. [Fries, Lo(/ik, § 124.] 



LECTURES ON LOGIC. 67 

sciousness, or the facts of miud : others on the pre- lect, 



XXVII. 



sentations of Sensitive Perception, or the facts of - 
nature. The former are the Mental Sciences, the Real Sci- 
hatter the Material. The facts of mind are given iuciuded'^the 
partly as contingent, partly as necessary ; the latter, — Matei^iai." 
the necessary facts, — are universal virtually and in 
themselves ; the former, — the contingent facts, — only 
obtain a fictitious universality by a process of gener- 
alisation. The facts of nature, however necessary in 
themselves, are given to us only as contingent and 
isolated phsenomena; they have, therefore, only that 
conditional, that empirical, generality, which we bestow 
on them by classification. 

Real truth is, therefore, the correspondence of our How can we 
thoughts with the existences which constitute their there is a 

, . -r~> 1 T rv ^ • TT correspouJ- 

objects. But here a dimculty arises; — How can we eme be- 
know that there is, that there can be, such a corre- thought and 
spondence'? All that we know of the objects is through '^° ^^'^ ' 
the presentations of our faculties ; but whether these 
present the objects as they are in themselves, we can 
never ascertain, for to do this it would be requisite to 
go out of ourselves, — out of our faculties, — to obtain a 
knowledge of the objects by other faculties, and thus 
to compare our old presentations with our new. But 
all this, even were the supposition possible, would be 
incompetent to afford us the certainty required. For 
were it possible to leave our old, and to obtain a new, 
set of faculties, by which to test the old, still the 
veracity of these new faculties would be equally ob- 
noxious to doubt as the veracity of the old. For 
what guarantee could we obtain for the credibility in 
the one case, which we do not already possess in the 
other 1 The new faculties could only assert their own 
truth ; but this is done by the old; and it is impos- 



68 LECTURES ON LOGIC. 

LECT. sible to imagine any presentations of the non-ego by 

^ '- any finite intelligence, to which a doubt might not be 

raised, whether these presentations were not merely 
subjective modifications of the conscious ego itself. 
All that could be said in answer to such a doubt is, 
that if such were true, our whole nature is a lie, — a 
supposition w^hich is not, without the strongest evi- 
dence, to be admitted ; and the argument is as com- 
petent against the sceptic in our present condition, as 
it would be were we endowed with any other con- 
ceivable form of Acquisitive and Cognitive Faculties. 
But I am here trench hig on what ought to be re- 
served for an explanation of the Criterion of Truth. 
Real Such, as it appears to me, is the only rational divi- 

it™ubcirvi- sion of Truth, according to the different character of 
the objects to which thought is relative, — into Formal 
and into Real Truth. Formal Truth, as we have seen, 
is subdivided into Logical and into Mathematical. 
Real Truth might likewise be subdivided, were this 
Metapiiysi- rcquisitc, into various species. For example. Meta- 
physical Truth might denote the harmony of thought 
Psychoiogi- with the necessary facts of mind ; Psychological 
Truth, the harmony of thought with the contingent 
Physical, facts of miud ; and Physical Truth, the harmony of 

thought with the phcenomena of external experience. 
Various ap- It uow rcmaius to say a word in regard to the con- 
the term fuslou which has bccu introduced into this subject, by 
the groundless distinctions and contradictions of philo- 
sophers. Some have absurdly given the name of iridh 
to the mere reality of existence, altogether abstracted 
from any conception or judgment relative to it, in any 
intelligence human or divine. In this sense physical 
truth has been used to denote the actual existence of 
a thing. Some have given the name of mctcipliysical 



I 



LECTURES ON LOGIC. 69 

truth to the con2:ruence of tlie thino; with its idea in lect. 

XXVII 

the mind of the Creator. Others again have bestowed '- 



the name of metaphysical truth on the mere logical 
possibility of being thought ; while they have deno- 
minated by logical truth the metaphysical or physical 
correspondence of thought with its objects. Finally, 
the term moral or ethical truth has been given to 
veracity, or the correspondence of thought with its 
expression. In this last case, truth is not, as in the 
others, employed in relation to thought and its object, 
but to thouo;ht and its enouncement. So much for the 
notion, and the principal distinctions of Truth. 

But returnino; to the parao-raph, I take the next The crite- 

'^ 1-1 rionof 

clause, which is, — ' The Criterion of truth is the neces- Truth, 
sity determined by the laws which govern our faculties 
of knowledge ; and the consciousness of this necessity is 
certainty.' That the necessity of a cognition, that 
is, the impossibility of thinking it other than as it 
is presented, — that this necessity, as founded on the 
laws of thought, is the criterion of truth, is shown 
by the circumstance, that where such necessity is 
found, all doubt in regard to the correspondence of 
the cognitive thought and its object must vanish ; 
for to doubt whether what we necessarily think in a 
certain manner, actually exists as we conceive it, is 
nothing less than an endeavour to think the necessary 
as the not necessary or the impossible, which is con- 
tradictory. 

What has just been said also illustrates the truth of 
the next sentence of the paragraph, — viz. ' Certainty or 
the conscious necessity of a cognition absolutely ex- 
cludes the admission of any opposite supposition. 
When such is found to be admissible, doubt and un- 
certainty arise.' This sentence requiring no explan- 



70 LECTURES ON LOGIC. 

LECT. ation, I proceed to the next — viz., * If we consider 
•^^^"' truth by relation to the degree and kind of Certainty, 



we have to distinguish Knowledge, Belief, and Opinion. 
Knowledge and Belief differ not only in degree but 
in kind. Knowledge is a certainty founded on intui- 
tion. Belief is a certainty founded upon feeling. The 
one is perspicuous and objective, the other is obscure 
and subjective. Each, however, supposes the other, 
and an assurance is said to be a knowledge or a belief, 
according as the one element or the other prepon- 
derates.' 
Knowledge In reference to this passage, it is necessary to say 
— their dif- something in regard to the difference of Knowledge 
and Belief. In common language the word Belief is, 
often used to denote an inferior degree of certainty. 
That the We may, however, be equally certain of what we be- 
au know-° lieve as of what we know, and it has, not without 
ultimately ground, bccu maintained by many philosophers, both 
intoa'cer- vci aucicut aud in modern times, that the certainty of 
Belief, all knowledge is, in its ultimate analysis, resolved into 
by Luther, a ccrtaiuty of belief. " All things," says Luther, " stand 
in a belief, in a faith, which we can neither see nor 
comprehend. The man who would make these visible, 
manifest and comprehensible, has vexation and heart- 
grief for his reward. May the Lord increase Belief in 
you and in others." ° But you may perhaps think that 
the saying of Luther is to be taken theologically, and 
that, philosophically considered, all belief ought to be 
founded on knowledo;e, not all knowledo-e in belief. 
But the same doctrine is held even by those philo- 
sophers who are the least disposed to mysticism or 
Aristotle, blind faith. Among these Aristotle stands distin- 

a Wchhclt, Th. iii. Abth. 2. Worls, p. 778.— Ed. 
Quoted by Sir W. Hamilton, RdiVs 



LECTUKES ON LOGIC. 71 

giiisbecL He defines science, strictly so called, or the lect. 

knowledge of indubitable truths, merely by the inten- — 1 

sity of our conviction or subjective assurance ; "" and 
on a primary and incomprehensible belief he hangs 
the whole chain of our comprehensible or mediate 
knowledge. The doctrine which has been called The 
Philosophy of Common Sense, is the doctrine which 
founds all our knowledge on belief ; and, though this 
has not been signalised, the doctrine of Common Sense 
is perhaps better stated by the Stagirite than by 
any succeeding thinker. " "What," he says, " appears 
to all men, that we affirm to be, and he who rejects 
this belief (Trtcrrt?) will assuredly advance nothing 
better worthy of credit." This passage is from his 
Nicomachean Etldcs.^ But, in his Physical Treatises, 
he founds in belief the knowledge we have of the re- 
ality of motion, and by this, as a source of knowledge 
paramount to the Understanding, he supersedes the 
contradictions which are involved in our conception 
of motion, and which had so acutely been evolved by 
the Eleatic Zeno, in order to show that motion was 
impossible."^ In like manner, in his Logical Treatises, 
Aristotle shows that the primary or ultimate princi- 
ples of knowledge must be incomprehensible ; for if 
comprehensible, they must be comprehended in some 
higher notion, and this again, if not itself incompre- 
hensible, must be again comprehended in a still higher, 
and so on in a progress ad iiifinitimi, which is absurd.^ 
But what is given as an ultimate and incomprehen- 
sible principle of knowledge, is given as a fact, the exist- 

a Various passages from Aristotle 7 B. viii. c. 3. See RekVs Worlcs, 

to this effect are cited by the Author, ^. 773. — Ed. 

Re'id's Worlcs, p. 771. — Ed. 5 Mctaphys., iii. (iv.) i. Cf. Anal. 

& B. X. c, 2.— Ed. Post, i. 2, 3.— Ed. 



72 LECTURES ON LOGIC. 

LECT. ence of whicli we must admit, but the reasons of whose 
■^ '- existence we cannot know, — we cannot understand. 



But such an admission, as it is not a knowledge, must 
be a belief ; and thus it is that, according to Aristotle, 
all our knowledge is in its root a blind, a passive faith, 
in other words, a feeling. The same doctrine was 
subsequently held by many of the acutest thinkers of 

The riaton- aucicnt times, more especially among the Platonists ; 

Procius. and of these Proclus is perhaps the philosopher in 
whose works the doctrine is turned to the best account." 
In modern times we may trace it in silent operation, 
though not explicitly proclaimed, or placed as the 
foundation of a system. It is found spontaneously 
recognised even by those who might be supposed the 
least likely to acknowledge it without compulsion. 

Hume. Hume, for example, against whose philosophy the 
doctrine of Common Sense was systematically ar- 
rayed, himself pointed out the weapons by which his 
adversaries subsequently assailed his scepticism ; for 
he himself was possessed of too much philosophical 
acuteness not to perceive that the root of knowledge 
is belief. Thus, in his Inquiry, he says — " It seems 
evident that men are carried by a natural instinct 
or prepossession to repose faith in their senses : and 
that, without any reasoning, or even almost before the 
use of reason, we always suppose an external universe 
which depends not on our preception, but would exist 
though we and every sensible creature were absent or 
annihilated. Even the animal creation are governed 
by a like opinion, and preserve this belief, — the belief 
of external objects, in all their thoughts, designs, and 
actions .... This very table, which we see 

o III Platoiiis Theologiam, i. c. 25. Quoted in Rekl's Works, p. 776. — Eij. 



LECTURES ON LOGIC. 73 

wliite, and which we feel hard, is believed to exist lect. 

XXVIT 

independent of our perception, and to be something 



external to our mind which perceives it." * 

But, on the other hand, the manifestation of this The mani- 

•11 11 r festation of 

belief necessaruy involves knowledge ; lor we cannot Belief in- 
believe without some consciousness or knowledge of Knowledge. 
the belief, and, consequently, without some conscious- 
ness or knowledge of the object of the belief. Now, 
the immediate consciousness of an object is called an intuition, - 

what. 

intuition, — an insight. It is thus impossible to separ- 
ate belief and knowledge, — feeling and intuition. 
They each sui3pose the other. 

The consideration, however, of the relation of Belief The qucs- 

111 T • ^^^^ ^^ '** 

and Knowledo;e does not properly belong; to Lome, the relation 

'^ .. rr./ '^ '^of Belief 

except in so far as it is necessary to explain the nature an<i Kuow- 

. lodge pro- 

of Truth and Error, It is alto2;ether a metaphysical periy mcta- 

. , physical. 

discussion ; and one of the most difficult problems of 
which Metaphysics attempts the solution. 

The remainder of the paragraph contains the state- 
ment of certain distinctions and the definition of cer- 
tain terms, which it was necessary to signalise, but 
which do not require any commentary for their illus- 
tration. The only part that might have required an 
explanation is the distinction of Truth into Pure, or 
a 2^'>'iori, and into Empirical, or a posteriori. The 
explanation of this division has been already given 
more than once in the course of the Lectures,^ but the 
following may now be added. 

Experience presents to us only individual objects, Pme and 

1 , .-,..-,-,-,. .-. .1 Empirical 

and as these individual objects might or might not Truth. 

a Inquiry concerning the Human ^)A_f/s/cs, vol. ii. p. 194 et seq. Cf. 

Understanding, sect. 12. Philosophi- Esser, Logik, §§ 4, 171. — Ed. [Fries, 

cal Works, iv. p. 177.— Ed. Logik, % 124.] 

/3 See above, Lectures on Meta- 



74 LECTURES ON LOGIC. 

LECT. have come within our sphere of observation, our whole 
'^"^^"' knowledge of and from these objects might or might 
not exist ; — it is merely accidental or contingent. But 
as our knowledge of individual objects affords the 
possibility, as supplying the whole contents, of our 
generalised or abstracted notions, our generalised or 
abstracted notions are, consequently, not more neces- 
sary to thought, than the particular observations out of 
which they are constructed. For example, every horse 
I have seen I might not have seen ; and I feel no more 
necessity to think the reality of a horse than the 
reality of a hippogriff ; I can, therefore, easily anni- 
hilate in thought the existence of the whole species. 
I can suppose it not to be, — not to have been. The 
case is the same with every other notion which is 
mediately or immediately the datum of observation. 
We can think away each and every part of the know- 
ledge we have derived from experience ; our whole em- 
pirical knowledge is, therefore, a merely accidental 
possession of the mind. 

But there are notions in the mind of a very different 
character, — notions which we cannot but think, if we 
think at all. These, therefore, are notions necessary 
to the mind ; and, as necessary, they cannot be the 
product of experience. For example, I perceive some- 
thing to begin to l)e. I feel no necessity to think 
that this thing must be at all, but thinking it exist- 
ent, I cannot but think that it has a cause. The no- 
tion, or rather the judgment, of Cause and Effect is, 
therefore, necessary to the mind. If so, it cannot be 
derived from experience. 



LECTURES ON LOGIC. 75 



LECTUEE XXVIII. 

MODIFIED STOICHEIOLOGY. 
SECTION I. — DOCTRINE OF TRUTH AND ERROR. 

SECTION II. ERROR, ITS CAUSES AND REMEDIES. 

A. — GENERAL CIRCUMSTANCES — SOCIETY. 

I NOW proceed to the consideration of the opposite lect. 

... XXVIII. 

of Truth, — Error, and, on this subject, give you the 

following paragraph. 

H XCI. Error is opposed to Truth ; and Error Par. xci. 
arises, 1°, From the commutation of what is Sub- charaJter 
jective with what is Objective in thought ; — 
2°, From the Contradiction of a -supposed know- 
ledge with its Laws; or, 3°, From a want of Ade- 
quate Activity in our Cognitive Faculties. 

Error is to be discriminated from Ignorance 
and from Illusion: these, however, along with 
Arbitrary Assumption, afford the most frequent 
occasions of error. '^ 



This paragraph consists of two parts, and these I Expiiea- 
shall successively consider. The first is — ' Error is 

o Twesteu, Die Lofjik, tniesondcre Ruiz, Cominentarius cle Scieiitia, &c. 
die Analutik,%% 308,^09. Ed. [Cf. Disp. xcii. p. 925.] 



76 LECTURES ON LOGIC. 

LECT. opposed to truth; and Error arises, 1°, From the 

^-1 1 commutation of what is subjective with what is ob- 
jective in thought ; 2°, From the contradiction of a 
supposed knowledge with its laws ; or, 3°, From a 
want of adequate activity in our cognitive faculties.' 

Error,— " In thc first placc, we have seen that Truth is the 

agreement of a thought with its object. Now, as 
Error is the opposite of truth, — Error must necessarily 
consist in a want of this aoreement. In the second 
place, it has been shown, that the criterion or stand- 
ard of truth is the necessity founded on the laws of 
our cognitive faculties ; and from this it follows that 
the essential character of error must be, either that it 
is not founded on these laws, or that it is repugnant to 
them. But these two alternatives may be viewed as 
only one ; for inasmuch as, in the former case, the 
judgment remains undecided, and can make no pre- 
tence to certainty, it may be thrown out of ac- 
count no less than in the latter, where, as positively 
contradictory of the laws of knowledge, it is neces- 

As Material, sarily false. Of these statements the first, that is, the 
non-agreement of a notion with its object, is error 
viewed on its material side ; and as a notion is the 
common product, — the joint result, afforded by the 
reciprocal action of object and subject, it is evident 
that whatever the notion contains not correspondent 
to the object, must be a contribution by the thinking 
subject alone, and we are thus warranted in saying 
that Material Error consists in the commuting of 
what is subjective with what is objective in thought ; 
in other words, in mistaking an ideal illusion for a 

As Formal, real representation. The second of these statements 
that is, the incongruence of the supposed cognition 
with the laws of knowledge, is error viewed on its 



LECTURES ON LOGIC. 77 

formal side. Now liere the question at once presents lect. 

XXVIII. 

itself, — How can an act of cognition contradict its 



own laws 1 Tlie answer is that it cannot ; and error, Arises from 

, , , , • • T ' n 1 1 1 the want of 

when more closely scrutinised, is lound not so much adequate 

1 1 T j_ • • r ' activity of 

to consist m the contradictory activity oi our cogm- the Cogni- 
tive faculties as in their want of activity. And this ties, 
may be in consequence of one or other of two causes. 
For it may arise from some other mental power, — the 
will, for example, superseding, — taking the place of, 
the defective cognition, or, by its intenser force, turn- 
ing it aside and leading it to a false result ; or it may 
arise from some want of relative perfection in the ob- 
ject, so that the cognitive faculty is not determined by 
it to the requisite degree of action. 

" What is actually thought, cannot but be correctly 
thought. Error first commences when thiuking is re- 
mitted, and can in fact only gain admission in virtue 
of the truth which it contains ; — every error is a per- 
verted truth. Hence Des Cartes " is justified in the 
establishment of the principle, — that we would never 
admit the false for the true, if we would only give 
assent to what we clearly and distinctly apprehend. — 
' Nihil nos unquam falsum pro vero admissuros, si 
tantum iis assensum pr?ebeamus, quse clare et dis- 
tincte percipimus.'" /^ In this view the saying of the 
Roman poet : — 

" Xam neqiie decipitur ratio, nee decipit iinquam," 7 

— is no longer a paradox ; for the condition of error 
is not the activity of intelligence, but its inactivity. 

So much for the first part of the paragraph. The Error dis- 

,. -,-, . ,,... -, f, -f criminated 

second is — Jiirror is to be discriminated irom Ignor- from ignor- 

a Prlncipia Philosophlce, i. 43. Cf. /3 Twesten, Logik, § 308. — Ed. 
Med. iv. De Vero et Falso. y Mauilius, ii. 131. — Ed. 



78' LECTURES ON LOGIC. 

LECT. ance and from Illusion, which, however, along with 
1 Arbitrary Assumption, afford the usual occasions of 

ance and -n j 

niusion. Jiirror. 

Ignorance. " Ignoraucc is a mere negation, — a mere not-know- 
ledge ; whereas in error there lies a positive pretence 
to knowledge. Hence a representation, be it imper- 
fect, be it even without any correspondent objective 
reality, is not in itself an error. The imagination of 
a hippogriff is not in itself false ; the Orlando Furioso 
is not a tissue of errors. Error only arises when we 
attribute to the creations of our minds some real 
object, by an assertory judgment; w^e do not err and 
deceive either ourselves or others, when we hold and 
enounce a subjective or problematic supposition only 
for what it is. Ignorance, — not-knowledge, — however, 
leads to error, when we either regard the unknown as 
non-existent, or when we falsely fill it up. The latter 
is, however, as much the result of Will, of arbitrary 
assumption, as of ignorance; and, frequently, it is the 
result of both together. In general, the will has no 
inconsiderable share in the activity b}?" which know- 
ledge is realised. The will has not immediately an 
influence on our judgment, but mediately it has. 
Attention is an act of volition, and attention fur- 
nishes to the Understanding the elements of its deci- 
sion. The will determines whether we shall carry on 
our investigations, or break them off, content with the 
first apparent probability ; and whether we shall apply 
our observations to all, or, only partially, to certain, 
momenta of determination. 

Illusion. " The occasions of Error which lie in those qualities 

of Presentation, Representation, and Thought arising 
from the conditions and influences of the thinking 



LECTURES ON LOGIC. 'TO 

subject itself, are called Illusions. But the existence lect. 
of illusion does not necessarily imply the existence of ^^^' 
error. Illusion becomes error only when we attribute 
to it objective truth ; whereas illusion is no error 
when we regard the fallacious appearance as a mere 
subjective affection. In the jaundice, we see every- 
thing tinged with yellow, in consequence of the suf- 
fusion of the eye with bile. In this case, the yellow 
vision is illusion ; and it would become error, were 
we to suppose that the objects we perceive were really 
so coloured. All the powers which co-operate to the its sources. 
formation of our judgments, may become the sources 
of illusion, and, consequently, the occasions of error. 
The Senses,* the Presentative Faculties, External and 
Internal, the Eepresentative, the Retentive, the Repro- 
ductive, and the Elaborative, Faculties, are immediate, 
the Feelings and the Desires are mediate, sources of 
illusion. To these must be added the Faculty of 
Signs, in all its actual manifestations in language. 
Hence we speak of sensible, psychological, moral, and 
symbolical, illusion."/^ In all these relations the causes 
of illusion are partly general, partly particular ; and 
though they proximately manifest themselves in some 
one or other of these forms, they may ultimately be 
found contained in the circumstances by which the 
mental character of the individual is conformed. 
Taking, therefore, a general view of all the possible 

a La Fontaine. See Mazui-e, Cours alites de la science aux apparences 

de Plillosophle, ii. 241. [Toutes les factices que nos sens nous suggerent. 

sciences naturelles ne sont autre C'est ce que La Fontaine a tr6s bien 

chose qu'une guerre -ouverte de la- exprime dans les vers suivant : 

raison coutre les deceptions de la " Quand I'eau courbe un baton, ma 

seusibilite c'est-a-dire, qu'elles raison le redresse," &c.^Ed. 

ont pour objet de reformer les erreurs /3 [Twesten, Logik, § 309, p. 288- 

de nos sens, et de substituer les re- 289, Cf. Sigwart, Lo'jik, §§ 484, 485.] 



80 



LECTURES ON LOGIC. 



LECT, 
XXVIII. 



Bacon's 
classifica- 



Sources of Error, I think they may be reduced to the 
following classes, which, as they constitute the heads 
and determine the order of the ensuing discussion, I 
shall comprise in the following paragraph, with which 
commences the consideration of the Second Chapter of 
Modified Logic. Before, however, proceeding to coii- 
ti'oroTtihe sider these several classes in their order, 1 may observe 
error. that Bacou is the first philosopher who attempted a 
systematic enumeration of the various sources of error; "" 
and his quaint classification of these, under the signi- 
ficant name of idols, into the four genera of Idols of 
the Tribe {idola trihiis). Idols of the Den, [idola specus), 
Idols of the Forum {idola fori), which may mean 
either the marketplace, the bar, or the place of public 
assembly, and Idols of the Theatre, {idola theatri), he 
thus briefly characterises. 



Par. XCII. 

Error, — its 



H XCII. The Causes and Occasions of Error 
are comprehended in one or other of the four 
following classes. For they are found either, 
1°, In the General Circumstances which modify 
the intellectual character of the individual ; or, 
2°, In the Constitution, Habits, and Eeciprocal 
Relations of his powers of Cognition, Feeling, 
and Desire ; or, 3°, In the Language which he 
employs, as an Instrument of Thought and a 
Medium of Communication ; or, 4°, In the nature 
of the Objects themselves, about which his know- 
ledge is conversant. 



Par.XCIII. 
I. General 
circumstan- 
ces which 



IT XCIII. Under the General Circumstances 
which modify the character of the individual, are 



o NovKin Or(janum, i. Aph. xxxix. — Ed. 



LECTURES ON LOGIC. 81 

comprehended 1°. The particular degree of Culti- lect. 

vation to which his nation has attained ; for its -1 '. 

rudeness, the partiality of its civilisation, and its ^aJ^^Jte?^ 
over-refinement are all manifold occasions of°[j^^j'°'^'" 
error ; and this cultivation is expressed not 
merely in the state of the arts and sciences, but 
in the degree of its religious, political, and social 
advancement ; 2°. The Stricter Associations, in so 
far as these tend to limit the freedom of thought, 
and to give it a one-sided direction : such are 
Schools, Sects, Orders, Exclusive Societies, Cor- 
porations, Castes, &c. — " 



In the commencement of the Course, I had occasion ExpHca- 
to allude to the tendency there is in man to assimilate Man by 
in opinions and habits of thought to those with whom social, and 
he lives.'^ Man is by nature, not merely by acciden- by the 
tal necessity, a social being. For only in society does his feiiows. 
he find the conditions which his difierent faculties 
require for their due development and application. 
But society, in all its forms and degrees, from a family 
to a State, is only possible under the condition of a 
certain harmony of sentiment among its members ; 
and as man is by nature destined to a social existence, 
he is by nature determined to that analogy of thouglit 
and feeling which society supposes, and out of which 
society springs. There is thus in every association, 
great and small, a certain gravitation of opinions 
towards a common centre. As in our natural body 
every part has a necessary sympathy with every 
other, and all together form, by their harmonious 
conspiration, a healthy whole ; so, in the social body, 

o Bacbmann, Logilc, §§ 402, 403.— )3 See Lectures on Metaphysics, vol. 
Ed. i. p. 48.— Ed. 

VOL. IL F 



82 LECTURES ON LOGIC. 

LECT. there is always a strong predisposition in each of its 

11 '. members to act and think in unison with the rest. 

This universal sympathy or fellow-feeling is the prin- 
ciple of the different S23irit dominant in different ages, 
countries, ranks, sexes, and periods of life. It is the 
cause why fashions, why political and religious en- 
thusiasm, why moral example either for good or evil, 
spread so rapidly and exert so powerful an influence. 
As men are naturally prone to imitate others, they, 
consequently, regard as important or insignificant, as 
honourable or disgraceful, as true or false, as good or 
bad, what those around them consider in the same 
light." 
Pascal Of the various testimonies I formerly quoted, ol 

quoted on . ., . . ^ „ -■ 

the power the stroug assimilatiug influence oi man on man, and 
of the power of custom to make that appear true, 
natural, and necessary, which in reality is false, un- 
natural, and only accidentally suitable, I shall only 
adduce that of Pascal, " In the just and the unjust," 
says he, " we find hardly anything which does not 
change its character in changing its climate. Three 
degrees of an elevation of the pole reverses the whole of 
jurisprudence. A meridian is decisive of truth, and a 
few years, of possession. Fundamental laws change. 
Right has its epochs. A pleasant justice which a river 
or a mountain limits ! Truth on this side the Pyre- 
nees, error on the other ! "'^ It is the remark of an in- 
genious philosopher, " that if we take a survey of the 
universe, all nations will be found admiring only the 
reflection of their own qualities, and contemning in 



of custom. 



a. [Wcmers, Unters'urhungen iiher die (vol. ii. p. 126, ed. Faugere.) Com- 

Denhkriifte unci Willenslcrdfte clcs pare Lectures on Metaphysics, vol. i, 

M enschen, ii. Z22.] p. 86.— Ed. 

^ Pensces, partie i. art. vi, § 8, 



I 



LECTURES ON LOGIC. 83 

others whatever is contrary to what they are acciis- lect. 

. XXVIIL 

tomed to meet with am on 2; themselves. Here is the — 1 

EngUshman accusing the French of frivolity ; and 
here the Frenchman reproaching the Englishman with 
selfishness and brutality. Here is the Arab persuaded 
of the infallibility of his Caliph, and deriding the 
Tartar who believes in the immortality of the Grand 
Lama. In every nation we find the same congratula- 
tion of their own wisdom, and the same contempt of 
that of their neio;hbours. 

" Were there a sage sent down to earth from heaven, 
who regulated his conduct by the dictates of pure rea- 
son alone, this sage would be universally regarded as 
a fool. He would be, as Socrates says, like a physi- 
cian accused by the pastry-cooks, before a tribunal of 
children, of prohibiting the eating of tarts and cheese- 
cakes ; a crime undoubtedly of the highest magnitude 
in the eyes of his judges. In vain would this sage 
support his opinions by the clearest arguments, — the 
most irrefragable demonstrations ; the whole world 
would be for him like the nation of hunchbacks, 
among whom, as the Indian fabulists relate, there 
once u23on a time appeared a god, young, beautiful, 
and of consummate symmetry. This god, they add, 
entered the capital ; he was there forthwith sur- 
rounded by a crowd of natives ; his figure appeared 
to them extraordinary ; laughter, hooting, and taunts 
manifested their astonishment, and they were about 
to carry their outrages still further ; had not one of 
the inhabitants (who had undoubtedly seen other 
men), in order to snatch him from the danger, sud- 
denly cried out — ' My friends ! my friends ! What 
are we going to do 1 Let us not insult this miserable 
monstrosity. If heaven has bestowed on us the gene- 



84 LECTURES ON LOGIC. 

LECT. ral gift of beauty, — if it has adorned our backs with 

1 '. a mount of flesh, let us with pious gratitude repair to 

the temple and render our acknowledgment to the 
immortal gods." This fable is the history of human 
vanity. Every nation admires its own defects, 
and contemns the opposite qualities in its neighbours. 
To succeed in a country one must be a bearer of 
the national hump of the people among whom he 
sojourns. 
The art of Thcrc are few philosophers who undertake to make 
wdi diffi- their countrymen aware of the ridiculous figure they 

cult to teach i*j1 i? ij_*ni? j1 j_' 

and to learn, cut lu the ejQ 01 rcasou ; and still lewer the nations 
who are able to profit by the advice. All are so punc- 
tiliously attached to the interests of their vanity, that 
none obtain in any country the name of wise, except 
those who are fools of the common folly. There is no 
opinion too absurd not to find nations ready to believe 
it, and individuals prompt to be its executioners or its 
martyrs. Hence it is that the philosopher declared, 
that if he held all truths shut up within his hand, he 
would take especial care not to show them to his 
fellow-men. In fact, if the discovery of a single 
truth dragged Galileo to the prison, to what punish- 
ment would he not be doomed who should discover 
all 1 Among those who now ridicule the folly of the 
human intellect, and are indignant at the persecution 
of Galileo, there are few who would not, in the age of 
that philosopher, have clamoured for his death. They 
would then have been imbued with different opinions ; 
and opinions not more passively adopted than those 
which they at present vaunt as liberal and enlight- 
ened. To learn to doubt of our opinions, it is suffi- 
cient to examine the powers of the human intellect, 
to survey the circumstances by which it is affected. 



LECTURES ON LOGIC. 85 

and to study the history of human follies. Yet in lect. 

. . XXVIII 

modern Europe six centuries elapsed from the foun- — 1 

dation of Universities until the appearance of that 
extraordinary man, — I mean Descartes, — whom his 
age first persecuted, and then almost worshipped as a 
demi-god, for initiating men in the art of doubting, — 
of doubting well,- — a lesson at which, however, both 
their scepticism and credulity show that, after two 
centuries, they are still but awkward scholars. Socrates 
was wont to say — " All that I know is that I know 
nothing." " In our age it would seem that men know 
everything except what Socrates knew. Our errors 
would not be so frequent were we less ignorant ; and 
our ignorance more curable, did we not believe our- 
selves to be all-wise. 

Thus it is that the influence of Society, both in 
its general form of a State or Nation, and in its par- 
ticular forms of Schools, Sects, &c., determines a 
multitude of opinions in its members, which, as they 
are passively received, so they are often altogether 
erroneous. 

Among the more general and influential of these Two genera 
there are two, which, though apparently contrary, are, influence of 
however, both, in reality, founded on the same in- L^prefudice 
capacity of independent thought, — on the same influ- |he oidT ** 
ence of example, — I mean the excessive admiration of 
the Old, and the excessive admiration of the New. 
The former of these prejudices,/^ — under which may be 
reduced the prejudice in favour of Authority, — was at 

a Plato, Apol., p. 23. — Ed. Errcurs et des Prejages repandus dans 

fi [On Prejudice in general see the la Soclete, Paris, 1810-1813, 3 vols, 

following works : — Dumarsais, Essai 8vo. J. L. Castillon, Essai sur les 

sur les Prejuges, new ed., Paris, 1822. Erreurs et les superstitions Anciennes 

Examen de V Essai sur les Prejuges, ei iV/oc^erwes, Amsterdam, 1765; Paris, 

Berl. 1777. Essai sur les Prejuges, 1767. Sir Thomas Brown, Vulgar 

Neuchiitel, 1796. J. B. Sulques, Des Errors, Glanvil, Essmjs.] 



86 LECTURES ON LOGIC. 

LECT. one time prevalent to an extent of which it is difficult 

LI 1 for us to form a conception. This prejudice is pre- 

Prepared by pared bj the vcrj education not only which we do, 
but which we all must, receive. The child necessarily 
learns everything at first on credit, — he believes upon 
authority. But when the rule of authority is once 
established, the habit of passive acquiescence and 
belief is formed, and, once formed, it is not again 
always easily thrown off. When the child has grown 
up to an age in which he might employ his own reason, 
he has acquired a large stock of ideas ; but who can 
calculate the number of errors which this stock con- 
tains '? and by what means is he able to discriminate 
the true from the false 1 Ilis mind has been formed 
to obedience and uninquiry ; he possesses no criterion 
by which to judge ; it is painful to suspect what has 
been long venerated, and it is felt even as a kind of 
personal mutilation to tear up what has become irra- 
dicated in his intellectual and moral being. Ponere 
difficile est quce ])lacuere diu. The adult does not, 
therefore, often judge for himself more than the child; 
and the tyranny of authority and foregone opinion 
continues to exert a sway during the whole course of 
his life. In our infancy and childhood the credit 
accorded to our parents and instructors is implicit ; 
and if what we have learned from them be confirmed 
by what we hear from others, the opinions thus re- 
commended become at length stamped in almost in- 
delible characters upon the mind. This is the cause 
why men so rarely abandon the opinions which vul- 
garly pass current ; and why what comes as new is 
by so many, for its very novelty, rejected as false. 
And hence it is, as already noticed, that truth is as it 
were geographically and politically distributed ; what 



LECTURES ON LOGIC. 87 

is truth on one side of a boundary beino; error and lect. 

absurdity on the other. What has now been said of — '. 

the influence of society at large, is true also of the 
lesser societies which it contains, all of which impose 
with a stronger or feebler, — a wider or more contracted, 
authority, certain received opinions upon the faith of 
the members. Hence it is that whatever has once 
obtained a recognition in any society, large or small, 
is not rejected when the reasons on which it was 
originally admitted, have been proved erroneous. It 
continues, even for the reason that it is old and has 
been accepted, to be accepted still ; and the title which 
was originally defective, becomes valid by continu- 
ance and prescription. 

But opposed to this cause of error, from the preju- 2. Prejudice 
dice in favour of the Old, there is the other, directly the New. 
the reverse, — the prejudice in favour of the New. 
This prejudice may be, in part at least, the result of 
sympathy and fellow-feeling. This is the cause why 
new opinions, however erroneous, if they once obtain 
a certain number of converts, often spread with a 
rapidity and to an extent which, after their futility 
has been ultimately showD, can only be explained on 
the principle of a kind of intellectual contagion. But 
the principal cause of the prejudice in favour of 
novelty lies in the Passions, and the consideration of 
these does not belong to the class of causes with 
which we are at present occupied. 

Connected with and composed of both these preju- Prejudice 
dices, — that in favour of the old and that in favour of Authority, 
the new, — there is the prejudice of Learned Authority; 
for this is usually associated with the prejudices of 
Schools and Sects. " As often as men have appeared, 
who, by the force of their genius, have opened up new 



88 LECTURES ON LOGIC. 

LECT. views of science, and thus contributed to the progress 

1 of the human intellect, so often have they, likewise, 

afforded the occasion of checking its advancement, 
and of turning it from the straight path of improve- 
ment. Not that this result is to be imputed as a re- 
proach to them, but simply because it is of the nature 
of man to be so affected. The views which influenced 
these men of genius, and which, consequently, lie at 
the foundation of their works, are rarely comprehended 
in their totality by those who have the names of these 
authors most frequently in their mouths. The many 
do not concern themselves to seize the ideal which a 
philosopher contemplated, and of which his actual 
works are only the imperfect representations ; they 
appropriate to themselves only some of his detached 
apophthegms and propositions, and of these compound, 
as they best can, a sort of system suited to their un- 
derstanding, and which they employ as a talisman in 
their controversies with others. As their reason is 
thus a captive to authority, and, therefore, unable to 
exert its native freedom, they, consequently, catch up 
the true and the false without discrimination, and 
remain always at the point of progress where they 
had been placed by their leaders. In their hands a 
system of living truths becomes a mere petrified or- 
ganism ; and they require that the whole science shall 
become as dead and as cold as their own idol. Such 
was Plato's doctrine in the hands of the Platonists ; 
such was Aristotle's philosophy in the hands of the 
Schoolmen ; and the history of modern systems affords 
equally the same result.'"* 

So much for the first genus into which the Sources 
of Error are divided. 

« Bachraann, Logik, § 404, p. 550. — Ed, 



LECTURES ON LOGIC. 89 



LECTUEE XXIX. 

MODIFIED STOICHEIOLOGY. 

SECTION II. — ERROR ITS CAUSES AND REMEDIES. 

A. — GENERAL CIRCUMSTANCES — SOCIETY. 

B, — AS IN POWERS OF COGNITION, FEELING, AND 

DESIRE. 

I. AFFECTIONS. PRECIPITANCY — SLOTH HOPE AND 

FEAR — SELF-LOVE. 



In our last Lecture, we entered on the consideration lect. 

XXIX 

of the various sources of Error. These, I stated, 



may be conveniently reduced to four heads, and con- ^^n!^'*^*" 
sist, 1°. In the General Circumstances which modify 
the intellectual character of the individual ; 2°. In the 
Constitution, Habits, and Eeciprocal Eelations of his 
powers of Cognition, Feeling, and Desire ; 3°. In the 
Language which he employs as an Instrument of 
Thought and a Medium of Communication ; and 4°. In 
the nature of the Objects themselves about which his 
knowledge is conversant. 

Of these, I then gave you a general view of the 
nature of those occasions of Error, which originate in 
the circumstances under the influence of which the 
character and opinions of man are determined for 
him as a member of society. Under this head I 



90 LECTURES ON LOGIC. 

LECT. stated, tliat, as man is destined by liis Creator to fulfil 

XXIX . • • 

L the end of his existence in society, he is wisely fur- 
nished with a disposition to imitate those among 
whom his lot is cast, and thus to conform himself to 
whatever section of human society he may by birth 
belong, or of which he may afterwards become a 
member. The education we receive, nay the very 
possibility of receiving education at all, supposes to a 
certain extent the passive infusion of foreign and tra- 
ditionary opinions. For as man is compelled to think 
much earlier than he is able to think for himself, — all 
education necessarily imposes on him many opinions 
which, whether in themselves true or false, are, in re- 
ference to the recipient, only prejudices ; and it is 
even only a small number of mankind, who at a later 
period are able to bring these obtruded opinions to 
the test of reason, and by a free exercise of their own 
intelligence to reject them if found false, or to acknow- 
ledge them if proved true. 

But while the mass of mankind thus remain, during 
their whole lives, only the creatures of the accidental 
circumstances which have concurred to form for them 
their habits and beliefs; the few who, are at last able 
to form opinions for themselves, are still dependent, 
in a great measure, on the unreasoning judgment 
of the many. Public opinion, hereditary custom, 
despotically impose on us the capricious laws of pro- 
priety and manners. The individual may possibly, in 
matters of science, emancipate himself from their ser- 
vitude ; in the affairs of life he must quietly submit 
himself to the yoke. The only freedom lie can here 
prudently manifest, is to resign himself with a con- 
sciousness that he is a slave not to reason but to con- 



I 



LECTURES ON LOGIC. 91 

ventional accident. And while he conforms himself lect. 

XXIX 

to the usages of his own society, he will be tolerant - 

to those of others. In this respect his maxim will be 
that of the Scythian prince : — " AVith you such may 
be the custom, — with us it is different." 

So much for the general nature of the influence to Means by 
which we are exposed from the circumstances of So- influence of 

111 society, as a 

ciety; it now remains to say what are the means by source of 
which this influence, as a source of error, may be be co'unter- 

- acted. 

counteracted. 

It has been seen that, in consequence of the man- Necessary 

-, . ^ • • /. 1 r 1 J.1 to institute 

ner m which our opinions are lormed lor us by tne a critical 

. T , p . , . T T -11 examination 

accidents ol society, our imposed and supposed know- of the con- 
ledge is a confused medley of truths and errors. knowLdge! 
Here it is evidently necessary to institute a critical 
examination of the contents of this knowledge. Des- 
cartes proposes that, in order to discriminate, among 
our prejudiced opinions, the truths from the errors, we 
ought to commence by doubting all." This has ex- 
posed him to much obloquy and clamour ; but most 
unjustly. The doctrine of Descartes has nothing Descartes, 
sceptical or offensive ; for he only maintains that it cept? '"^'^ 
behoves us to examine all that has been inculcated on 
us from infancy, and under the masters to whose 
authority we have been subjected, with the same at- 
tention and circumspection which we accord to dubi- 
ous questions. In fact there is nothing in the precept 
of Descartes, which had not been previously enjoined 
by other philosophers. Of these I formerly quoted to 
you several, and among others the remarkable testi- 
monies of Aristotle, St Augustin, and Lord Bacon./^ 

« Biscours de la Methode, Partie /3 See Lectures on Metaphysics, vol 
ii.— Ed. i. p. 90 et seq. — Ed. 



92 LECTURES ON LOGIC. 

LECT. But altliough there be notliiDg reprehensible in the 

. L precept of Descartes, as enounced by him, it is of 

Conditions less practical utility in consequence of no account 
dify i\s''"'" being taken of the circumstances which condition and 
application, ^^j-f^ '^g application. For, in the first place, the 
judgments to be examined ought not to be taken at 
random, but selected on a principle, and arranged in 
due order and dependence. But this requires no 
ordinary ability, and the distribution of things into 
their proper classes is one of the last and most diffi- 
cult fruits of philosophy. In the second place, there 
are among our prejudices, or pretended cognitions, 
a great many hasty conclusions, the investigation of 
which requires much profound thought, skill, and ac- 
quired knowledge. Now, from both of these consider- 
ations, it is evident that to commence philosophy by 
such a review, it is necessary for a man to be a philo- 
sopher before he can attempt to become one. The 
precept of Descartes is, therefore, either unreasonable, 
or it is too unconditionally expressed. And this latter 
alternative is true. 
A gradual What cau bc rationally required of the student of 

andprogres- ^ _ . . 

8ive abroga- phllosophy, Is uot a preliminary and absolute, but a 
judiccsaii gradual and progressive abrogation, of preiudices. It 

that can be ° ^ ^. , ^ . 

required of cau ouly bc rcqulrcd of him, that, when, in the course 
ofphiio- of his study of philosophy, he meets with a proposi- 
tion which has not been already sufficiently sifted, — 
(whether it has been elaborated as a principle or ad- 
mitted as a conclusion), — he should pause, discuss it 
without prepossession, and lay aside for future con- 
sideration all that has not been subjected to a search- 
ing scrutiny. The precept of Descartes, when rightly 
explained, corresponds to that of St Paul " : " If any 

o 1 Cor., iii. 18. 



LECTURES ON LOGIC. 93 

man amona; you seemetli to be wise in this world, let lect. 

. . XXIX. 

liim become a fool, that he may be wise ; " that is, let '- 

him not rely more on the opinions in which he has 
been brought up, and in favour of which he and those 
around him are prejudiced, than on so many visions 
of imagination ; and let him examine them with the 
same circumspection as if he were assured that they 
contain some truth among much falsehood and many 
extravagancies," 

Proceedina: now to the second class of the Sources 
of Error, which are found in the Mind itself, I shall 
commence with the following paragraph : — 



IF XCIV. The Sources of Error which arise Par. xciv. 
from the Constitution, Habits, and reciprocal of Error 

-i-» o 1 c r^ • • T\ T arising from 

Eelations of the powers of Cognition, Jb eelmg, the powers 
and Desire, may be subdivided into two kinds, tion, Feei- 

f> 1 • • 1 1 '"^S; and 

The first of these consists in the undue prepon- Desire,— of 
derance of the Affective Elements of mind, (the 
Desires and Feelings), over the Cognitive : the 
second, in the weakness or inordinate strength 
of some one or other of the Cognitive Faculties 
themselves. 



Afiection is that state of mind in which the Feel- Expiica- 
ings and Desires exert an influence not under the con- 1. Prcpon- 
trol of reason ; in other words, a tendency by which Affection 
the intellect is impeded m its endeavour to think an nition. 
object as that object really is, and compelled to think 
it in conformity with some view prescribed by the 
passion or private interest of the subject thinking. 

a This criticism of the precept of taken from Crousaz, Locjique, t. iiL 
Descartes is, with some slight changes, part ii., ch. 6, p. 263 et seq. — Ed. 



9i LECTUEES ON LOGIC. 

LECT. The human mind, when unruffled by passion, may 

L be compared to a calm sea. A calm sea is a clear 

mirror, in which the sun and clouds, in which the 
Influence of forms of heavcu and earth, are reflected back pre- 
tife Mbr cisely as they are presented. But let a wind arise ; 
and the smooth clear surface of the water is lifted 
into billows and agitated into foam. It no more re- 
flects the sun and clouds, the forms of heaven and 
earth, or it reflects them only as distorted and broken 
images. In like manner, the tranquil mind receives 
and reflects the world without as it truly is ; but let 
the wind of passion blow, and every object is repre- 
sented, not as it exists, but in the colours and aspects 
and partial phases in which it pleases the subject to 
regard it. The state of passion and its influence 
Boethius on the Cognitive Faculties are truly pictured by 
''"''''• Boethius.'^ 

" Nubibus atris 

Condita nullum Tu quoque si vis 

Fuudere possunt Lumine claro 

Sidera lumen. Cernere verum, 

Si mare volvens Tramite recto 

Turbidus auster Carpere callem : 

Misceat sestum, Gaudia pelle, 

Vitrea dudum, Pelle timorem. 

Parque serenis Spemque fugato, 

Unda diebus, Nee dolor adsit, 

Mox resoluto Nubila mens est, 

Sordida coeno, Viuctaque frenis, 

Visibus obstat. Hsec ubi regnant." 



Error Evcry error consists in this, — that we take some- 

limited to , . „ . . , , 

Provable thiug lor non-cxistcnt, because we have not become 



Reasoning. 



aware of its existence, and that, in place of this ex- 

a De ConsoL Phil, L. i., Metr. 7.— Ed. 



LECTURES ON LOGIC. 95 

istent something, we fill up the premises ot a probable lect. 
reasoning with somethiuo; else. 



I have here limited the possibility of error to Pro- 
bable Reasoning, for, in Intuition and Demonstration, 
there is but little possibility of important error. 
Hobbes indeed asserts that had it been contrary to the 
interest of those in authority, that the three angles of 
a triangle should be equal to two right angles, this 
truth would have been long ago proscribed as heresy, 
or as high treason." This may be an ingenious illus- 
tration of the blind tendency of the passions to sub- 
jugate intelligence ; but we should take it for more 
than was intended by its author, were we to take it 
as more than an ingenious exaggeration. Limiting, 
therefore, error to probable inference, (and this consti- 
tutes, with the exception of a comparatively small 
department, the whole domain of human reasoning), 
we have to inquire, How do the Passions influence us 
to the assumption of false premises ? To estimate the 
amount of probability for or against a given propo- 
sition, requires a tranquil, an unbiassed, a comprehen- 
sive, consideration, in order to take all the relative 
elements of judgment into due account. But this 
requisite state of mind is disturbed when any interest, 
any wish, is allowed to interfere. 

^ XCV. The disturbing Passions may be re- Par. xcv. 
duced to four : — Precipitancy, Sloth, Hope and sions, as 

sources of 

Fear, Self-love. Error,— 

o ' n -y ' ' t reduced to 

1 . A restless anxiety for a decision begets four. 
impatience, which decides before the preliminary 
inquiry is concluded. This is Precipitancy. 

a Leviathan, Pai't I. ch. 11. — Ed. 



96 LECTUKES ON LOGIC. 

LECT. 2°. The same result is the effect of Sloth, 

XXIX • • • 

L which dreams on in conformity to custom, with- 
out subjecting its beliefs to the test of active 
observation. 

3°. The restlessness of Hope or Fear impedes 
observation, distracts attention, or forces it only 
on what interests the passion ; — the sanguine 
looking only on what harmonises with his hopes, 
the diffident only on what accords with his 
fears. 

4°. Self-love perverts our estimate of proba- 
bility by causing us to rate the grounds of judg- 
^ ment, not according to their real influence on the 

truth of the decision, but according to their 
bearing on our personal interests therein. 

Expiica- In regard to Impatience or Precipitation, — "all is 
i.^Precipi- the cause of this which determines our choice on one 
*'^'"^^' side rather than another. An imagination excites 
pleasure, and because it excites pleasure we yield our- 
selves up to it. We suppose, for example, that we 
are all that we ought to be, and why '? Because this 
supposition gives us pleasure. This, in some disposi- 
tions, is one of the greatest obstacles to improvement ; 
for he who entertains it, thinks there is no necessity to 
labour in order to become what he is already. ' I be- 
Seneca. licvc,' says Scueca," ' that many had it in their power 
to have attained to wisdom, had they not been im- 
peded by the belief that wisdom they had already 
attained.' ' Multos puto ad sapientiam potuisse per- 
Erasmus. vcuire, uisl putasscut sc pervenissc.'" ^ Erasmus gives 

a De Tranquillitate Animi, c. 1.— $ Crousaz, Logique, t. iii., part. ii. 
Ed. ch. 7, p. 297.— Ed. 



LECTURES ON LOGIC. 97 

the following as tlie principal advice to a young lect, 
votary of learning in the conduct of his studies : " To — ' 
read the most learned books, to converse with the 
most learned men ; but, above all, never to conceit 
that he himself was learned." " 

" From the same cause, men flatter themselves with iiiustra- 
the hope of dying old, although few attain to longe- 
vity. The less probable the event the more certain 
are they of its occurrence ; and why 1 Because the im- 
agination of it is agreeable. ' Decrepiti senes pauco- From 

, . T ■ , • Seneca. 

rum annorum accessionem votis mendicant ; mmores 
natu seipsos esse fingunt : mendacio sibi blandiuntur: 
et tam libenter fallunt, quam si fata una decipiant.' " ^ 
" Preachers," says Montaigne, " are aware that the From 
emotion which arises during their sermons animates °^ '^'^ 
themselves to belief, and we are conscious that when 
roused to anger we apply ourselves more intently to 
the defence of our thesis, and embrace it with greater 
vehemence and approbation, than we did when our 
mind was cool and unruffled. You simply state your 
case to an advocate ; he replies w^ith hesitation and 
doubt : you are aware that it is indifferent to him 
whether he undertakes the defence of the one side or of 
the other ; but have you once fee'd him well to take 
your case in hand ; he begins to feel an interest in it, 
his will is animated. His reason and his science be- 
come also animated in proportion. Your case presents 
itself to his understandino; as a manifest and indubit- 
able truth ; he now sees it in a wholly different light, 

a " Joannes Alexander Brassicanus se doctum nunquam piitaret." Motto 

rogavit Erasmum, qua ratione doctus to G. J. Vossius, Opuscula de Studi- 

posset fieri, respondit ex tempore : orum Ratione. See Crenius, Consilia 

si doctis assidue conviveret, si doctos et Methodus, &c., p. 686, 1692. — Ed. 
audiret non minus submisse quam fi Heneca, De Brevitate Fito, c. 11. 

honorifice, si doctos strenue legeret, si Crousaz, Logique, t. iii. p. ii. ch. 7, p. 

doctos diligenter edisceret, denique si 297, ed. 1725. — Ed. 

VOL. TL G 



98 LECTUKES ON LOGIC. 

LECT. aud really believes that you have law and justice on 

XXIX . . 

'- your side." " It is proper to observe that Montaigne 

was himself a lawyer, — he had been a counsellor of the 
Parliament of Bordeaux. 
Precipitate It might scem that Precipitate Dogmatism and an 
anTETeptu inclination to Scepticism were opposite characters of 
o'/Kame^ mlud. They are, however, closely allied, if not merely 
isposi ion. pj^^ggg q£ ^j^g same disposition. This is indeed con- 
fessed by the sceptic Montaigne.^ "The most un- 
easy condition for me is to be kept in suspense on 
urgent occasions, and to be agitated between fear 
and hope. Deliberation, even in things of lightest 
moment, is very troublesome to me ; and I find 
my mind more put to it, to undergo the various 
tumbling and tossing of doubt and consultation, 
than to set up its rest, and to acquiesce in whatever 
shall happen, after the die is thrown. Few passions 
break my sleep ; but of deliberations, the least dis- 
turbs me." 
Remedy Prccipitatiou is no incurable disease. There is for 

tation.^"^' it one sure and simple remedy, if properly applied. 
It is only required, to speak with Confucius, manfully 
to restrain the wild horse of precipitancy by the curb 
of consideration, — to weigh the reasons of decision, 
each and all, in the balance of cool investigation, — not 
to allow ourselves to decide until a clear conscious- 
ness has declared these reasons to be true, — to be suffi- 
cient ; and, finally, to throw out of account the suf- 
frages of self-love, of prepossession, of passion, and to 
admit only those of reflection, of experience, and of 
evidence. This remedy is certain and effectual. In 
theory it is satisfactory, but its practical application 

a Essais, L. ii. ch. 12. Quoted by ;3 Essais, L. ii. c. 17. — Ed. 
Crousaz, l. c. — Ed. 



LECTURES ON LOGIC. 99 

requires a moral resolution, for the acquisition of lect. 

. . XXIX 

whicli no precept can be given. 



In the second place, "Sloth is likewise a cause of 2. sioth. 
precipitation, and it deserves the more attention as it 
is a cause of error extremely frequent, and one of 
which we are ourselves less aware, and which is less 
notorious to others. We feel it fatiguing to continue 
an investigation, therefore we do not pursue it ; but 
as it is mortifying to think that we have laboured in 
vain, we easily admit the flattering illusion that we 
have succeeded. By the influence of this disposition 
it often happens, that, after having rejected what first 
presented itself, — after having rejected a second time 
and a third time what subsequently turned up, be- 
cause not sufficiently applicable or certain, we get 
tired of the investigation, and perhaps put up with 
the fourth suggestion, which is not better, haply even 
worse, than the preceding ; and this simply because it 
has come into the mind when more exhausted and less 
scrupulous than it was at the commencement," « " The Senera 
volition of that man," says Seneca, " is often frus- 
trated, who undertakes not what is easy, but who 
wishes what he undertakes to be easy. As often as 
you attempt anything, compare together yourself, the 
end which you propose, and the means by which it is 
to be accomplished. For the repentance of an un- 
finished work will make you rash. And here it is of 
consequence whether a man be of a fervid or of a 
cold, of an aspiring or of a humble, disposition." ^ 

To remedy this failing it is necessary, in conform- its remedy, 
ity with this advice of Seneca, to consult our forces, 
and the time we can afibrd, and the difiiculty of the 

o Crousaz, Logique, t. iii. part ii. ch. j3 De Ira, L. iii. c. 7. Quoted by 
7, p. 302. — Ed. Crousaz, Logique, i. iii. p. 302. — Ed. 



100 LECTURES ON LOGIC. 

LECT. subjects on wliicli we enter. We ouglit to labour only 
'- at intervals, to avoid the tedium and disquiet conse- 



quent on unremitted application ; and to adjourn the 
consideration of any thought which may please us 
vehemently at the moment, until the prepossession in 
its favour has subsided with the animation which gave 
it birth. 
3. Hope The two Causes of premature judgment, — the affec- 
tions of Impatience and Sloth, — being considered, I pass 
on to the third principle of Passion, by which the in- 
tellect is turned aside from the path of truth, — I mean 
the disturbing influence of Hope and Fear. These 
passions, though reciprocally contrary, determine a 
similar effect upon the deliberations of the Under- 
standing, and are equally unfavourable for the in- 
terest of truth. In forming a just conclusion upon a 
question of probable reasoning, that is, where the 
grounds of decision are not few, palpable, and of de- 
terminate effect, — and such questions may be said to 
be those alone on which differences of opinion may 
arise, and are, consequently, those alone which re- 
quire for their solution any high degree of observation 
and ingenuity, — in such questions hope and fear 
exert a very strong and a very unfavourable influ- 
ence. In these questions it is requisite, in the first 
place, to seek out the premises ; and, in the second, 
to draw the conclusion. Of these requisites the first 
is the more important, and it is also by far the more 
difficult. 
How Hope Now the passious of Hope and Fear operate sever- 
operateun- ally to prcvcut the intellect from discovering all the 
on the\Tn- clemcuts of dccisiou, which ought to be considered in 

derstanding. p • ■ i • i • i • 

lormmg a correct conclusion, and cause it to take into 
account those only which harmonise with that con- 



LECTURES ON LOGIC. 101 

elusion to wliicli tlie actuating passion is inclined, lect. 

And here the passion operates in two ways. In the L 

first place, it tends so to determine the associations of 
thought, that only those media of proof are suggested 
or called into consciousness, which support the conclu- 
sion to which the passion tends. In the second place, 
if the media of proof by which a counter conclusion is 
supported, are brought before the mind, still the mind 
is influenced by the passion to look on their reality 
with doubt, and, if such cannot be questioned, to 
undervalue their inferential importance ; whereas it is 
moved to admit, without hesitation, those media of 
proof, which favour the conclusion in the interest of 
our hope or fear, and to exaggerate the cogency with 
which they establish this result. Either passion looks 
exclusively to a single end, and exclusively to the 
means by which that single end is accomplished. 
Thus the sanguine temperament, or the mind under 
the habitual predominance of hope, sees only and 
magnifies all that militates in favour of the wished- 
for consummation, which alone it contemplates ; 
whereas the melancholic temperament, or the mind 
under the habitual predominance of fear, is wholly 
occupied with the dreaded issue, views only what 
tends to its fulfilment, while it exaggerates the pos- 
sible into the probable, the probable into the certain. 
Thus it is that whatever conclusion we greatly hope or 
greatly fear, to that conclusion we are disposed to 
leap ; and it has become almost proverbial, that men 
lightly believe both what they wish, and what they 
dread, to be true. 

But the influence of Hope on our judgments, inclin- 
ing us to find whatever we wish to find, in so far as 
this arises from the illusion of Self-love, is compre- 



102 LECTURES ON LOGIC. 

LECT. headed in tliis, — the fourth cause of Error, — to which 

XXIX. T 1 

1 now proceed. 



4. Self-love. Sclf-lovc, uudcr wliich I inckide the dispositions of 
Vanity, Pride, and, in general, all those which incline 
us to attribute an undue weight to those opinions in 
which we feel a personal interest, is by far the most 
extensive and influential impediment in the way of 
reason and truth. In virtue of this principle, what- 
ever is ours, — whatever is adopted or patronised by 
us, whatever belongs to those to whom we are at- 
tached, — is either gratuitously clothed with a charac- 
ter of truth, or its pretensions to be accounted true 
are not scrutinised with the requisite rigour and im- 
partiality. I am a native of this country, and, there- 
fore, not only is its history to me a matter of peculiar 
interest, but the actions and character of my country- 
men are viewed in a very difierent light from that in 
which they are regarded by a foreigner. I am born 
and bred a member of a religious sect, and because 
they constitute my creed, I find the tenets of this 
sect alone in conformity to the Word of God. I am 
the partisan of a philosophical doctrine, and am, 
therefore, disposed to reject whatever does not har- 
monise with my adopted system. 

Aristotle,— It Is tlic part of a philosopher, says Aristotle, inas- 
' much as he is a philosopher, to subjugate self-love, 
and to refute, if contrary to truth, not only the opin- 
ions of his friends, but the doctrines which he himself 
may have professed." It is certain, however, that 
philosophers, — for philosophers are men, — have been 
too often found to regulate their conduct by the oppo- 

iiiustrations sitc principle. That man pretended to the name of 

cnce of Self- philosopher, who scrupled not to declare that he 

a Eth. Nic, i. 4 ((!).— Ed. 



LECTURES ON LOGIC. 103 

would rather be in the wrons: with Plato than in the lect. 

. . XXIX 

right with his opponents." " Gisbert Voetius urged 1 

Mersennus to refute a work of Descartes a year before opinioas. 
the book appeared, and before he had himself the 
means of judging whether the opinions it contained 
were right or wrong. A certain professor of philo- 
sopliy in Padua came to Galileo, and requested that he 
would explain to him the meaning of the term paral- 
laxis ; which he wished, he said, to refute, having 
heard that it was opposed to Aristotle's doctrine 
touching the relative situation of the comets. What ! 
answered Galileo, you wish to controvert a word 
the meaning of which you do not know I Redi 
tells us that a sturdy Peripatetic of his acquaint- 
ance would never consent to look at the heavens 
through a telescope, lest he should be compelled to 
admit the existence of the new stars discovered by 
Galileo and others. The same Redi informs us that 
he knew another Peripatetic, a staunch advocate of 
the Aristotelian doctrine of equivocal generation, (a 
doctrine, by the way, which now again divides the 
physiologists of Europe), and w^ho, in particular, main- 
tained that the green frogs which appear u2:>on a 
shower come down with the rain, who would not be 
induced himself to select and examine one of these 
frogs. And why '? Because he w-as unwilling to be 
convicted of his error, by Redi showing him the green 
matter in the stomach, and its feculse in the intestines 
of the animal."^ The spirit of the Peripatetic 
philosophy was, however, wholly misunderstood by 
these mistaken followers of Aristotle ; for a true 

a Cicero, Tusc. Qucest., i. 17. 1766, § 332. First published in 1756. 

/SReimarus, p. 389. [Die Vernunft- The above four anecdotes are all taken 

lehre, ron H.S.R. (Hermann Samuel from this work. — Ed.] 
lieimarus), dritte Auflnge, Hamburg, 



104 LECTURES ON LOGIC. 

LECT. Aristotelian is one who listens rather to the voice of 

XXIX 

^ ' ^ ' nature than to the precept of any master, and it is 
well expressed in the motto of the great French anato- 
mist, — Eiolanus est Peripateticus ; credit ea, et ea 
tantum, quse vidit. From the same principle pro- 
ceeds the abuse, and sometimes even the persecution, 
which the discoverers of new truths encounter from 
those whose cherished opinions these truths subvert. 
Self-love In like manner, as we are disposed to maintain our 

leads us to , . . , . , 1 • 1 p 1 

regard with owu opiuiou, WO arc mchnedto regard with favour the 
opinions of opiulous of thoso to whom we are attached by love, 
whom we gratitude, and other conciliatory affections. " We do 

are in any t • i i f c • i 

way attach- uot lunit our attachment to the persons of our friends, 
— we love in a certain sort all that belongs to them ; 
and as men generally manifest sufficient ardour in 
support of their opinions, we are led insensibly by a 
kind of sympathy to credit, to approve, and to defend 
these also, and that even more passionately than our 
friends themselves. We bear affection to others for 
various reasons. The agreement of tempers, of inclina- 
tions, of pursuits ; their appearance, their manners, 
their virtue, the partiality which they have shown to 
us, the services we have received at their hands, and 
many other particular causes, determine and direct our 
love. 

Male- " It is observed by the 2;reat Malebranche," that if 

branche n n • -i n 

adduced to auv of our fiicnds, — any even of those we are disposed 

this effect. "^ -^ . . ^ 

to love, — advance an opinion, w^e forthwith lightly 
allow ourselves to be persuaded of its truth. This 
opinion we accept and support, without troubling our- 
selves to inquire whether it be conformable to fact, 
frequently even against our conscience, in conformity 
to the darkness and confusion of our intellect, to the 

o Recherche clc la Vcrite, L. iv. ch. 13. — Ed. 



LECTURES ON LOGIC. 105 

corruption of our heart, and to the advantages which lect. 

XXIX 

we hope to reap from our facility and complaisance."" — ^ — ^ 
The influence of this principle is seen still more This shown 

^^ ^ especially 

manifestly when the passion chano-es ; for thous^h the when the 

'' -■■ ^ '-' ^ passion 

things themselves remain unaltered, our judgments changes, 
concerning them are totally reversed. How often do 
we behold persons who cannot, or will not, recognise 
a single good quality in an individual from the mo- 
ment he has chanced to incur their dislike, and who 
are even ready to adopt opinions, merely because 
opposed to others maintained by the object of their 
aversion "? The celebrated Arnauld/^ a;oes so far even Amauki 
as to assert, that men are naturally envious and jeal- man is 

1 . . . . , ^ 1 naturally 

ous ; that it is with pain they endure the contem- envious. 
plation of others in the enjoyment of advantages 
which they do not themselves possess ; and, as the 
knowledge of truth and the power of enlightening 
mankind is of one of these, that they have a secret in- 
clination to deprive them of that glory. This accord- 
ingly often determines them to controvert without a 
ground the opinions and discoveries of others. Self- 
love accordingly often argues thus : — ' This is an 
opinion which I have originated, this is an opinion, 
therefore, which is true ; ' whereas the natural 
malignity of man not less frequently suggests such 
another : ' It is another than I who has advanced this 
doctrine ; this doctrine is, therefore, false.' 

We may distinguish, however, from malignant or The love of 
envious contradiction another passion, which, though tion. 
more generous in its nature and not simply a mode of 
Self-love, tends, nevertheless, equally to divert us from 
the straight road of truth, — I mean Pugnacity, or the 

« Caro, Nouvelle Lofj'ique, part ii., ^ VArt de Penser {Port-Royal Lo- 
ch, viii., p. 288.— Ed. gic), p. iii. ch. 20 Ed. 



106 LECTURES ON LOGIC. 

LECT. love of Disputation. Under the influence of tins 
^^^ ' passion, we propose as our end victory, not truth. 



We insensibly become accustomed to find a reason for 
any ojoinion, and, in placing ourselves above all rea- 
sons, to surrender our belief to none. Thus it is why 
two disputants so rarely ever agree, and why a ques- 
tion is seldom or never decided in a discussion, where 
the combative dispositions of the reasoners have once 
been roused into activity. In controversy it is 
always easy to find wherewithal to reply ; the end 
of the parties is not to avoid error, but to impose 
silence ; and they are less ashamed of continuing 
wrong than of confessing that they are not right.'* 
These affec- Thcsc affcctions may be said to be tlie immediate 
immediate causcs of all crror. Other causes there are, but not 

causes of all . t , x n r • i . i 1 1 r 

error. immediate. In so lar as Logic detects the sources oi 
cond™onr^ our false judgments and shows their remedies, it must 
fo^'the ^ carefully inculcate that no precautionary precept for 
ofprecejts particular cases can avail, unless the inmost principle 
sources o^ of tlic cvil bc discovcrcd, and a cure applied. You 
must, therefore, as you would remain free from the 
hallucination of false opinion, be convinced of the ab- 
solute necessity of following out the investigation of 
every question calmly and without passion. You must 
learn to pursue, and to estimate, truth without distrac- 
tion or bias. To this there is required, as a primary 
condition, the unshackled freedom of thought, the 
equal glance which can take in the whole sphere of 
observation, the cool determination to pursue the 
truth whithersoever it may lead ; and, what is still 
more important, the disposition to feel an interest in 
truth, and in truth alone. If perchance some col- 
lateral interest may first prompt us to the inquiry, 

aL'Art de Penser, p. iii., ch. 20. ch. 9, p. 311, Paris, 1820.— Ed. 
Cf. CarOj Nouvclle Loglquc, part ii., 



error. 



LECTURES ON LOGIC. 107 

in our general interest for trutli we must repress, — lect. 

we must forget, this interest, until the inquiry be con- '. 

eluded. Of what account are the most venerated 
opinions if they be untrue 1 — At best they are only 
venerable delusions. He who allows himself to be 
actuated in his scientific procedure by any partial in- 
terest, can never obtain a comprehensive survey of the 
whole he has to take into account, and always, there- 
fore? remains incapable of discriminating, with accu- 
racy, error from truth. The independent thinker must, 
in all his inquiries, subject himself to the genius of 
truth, — must be prepared to follow her footsteps 
without faltering or hesitation. In the consciousness 
that truth is the noblest of ends, and that he pursues 
this end with honesty and devotion, he will dread no 
consequences, — ^for he relies upon the truth. Does he 
compass the truth, he congratulates himself on his 
success ; does he fall short of its attainment, he knows 
that even his present failure will ultimately advance 
him to the reward he merits. Err he may, and that 
perhaps frequently, but he will never deceive himself. 
We cannot, indeed, rise superior to our limitary na- 
ture, we cannot, therefore, be reproached for failure ; 
but we are always responsible for the calmness and 
impartiality of our researches, and these alone render 
us worthy of success. But though it be manifest, 
that to attain the truth we must follow whithersoever 
the truth may lead, still men in general are found to 
yield not an absolute, but only a restricted, obedience 
to the precept. They capitulate, and do not uncon- 
ditionally surrender. I give up, but my cherished 
dogma in religion must not be canvassed, says one ; — 
ray political principles are above inquiry, and must 
be exempted, says a second ; — my country is the land 
of lands, this cannot be disallowed, cries a third ; — 



108 



LECTUEES ON LOGIC. 



LECT. 
XXIX. 



my order, my vocation, is undoubtedly the noblest, 
exclaim a fourth and fifth ; — only do not require that 
we should confess our having erred, is the condition 
which many insist on stipulating. Above all, that 
resolve of mind is difficult, which is ready to sur- 
render all fond convictions, and is prepared to re- 
commence investigation the moment that a funda- 
mental error in the former system of belief has been 
detected. These are the principal grounds why, 
among men, opinion is so widely separated from 
opinion ; and why the clearest demonstration is so 
frequently for a season frustrated of victory. 



Par. xcvi. 

Rules 
against 
Errors from 
the Affec- 
tions. 



IT XCVI. Against the Errors which arise from 
the Affections, there may be given the three 
following rules : — 

1°. When the error has arisen from the influ- 
ence of an active affection, the decisive judg- 
ment is to be annulled ; the mind is then to be 
freed, as far as possible, from passion, and the 
process of inquiry to be recommenced as soon 
as the requisite tranquillity has been restored. 

2°. When the error has arisen from a relaxed 
enthusiasm for knowledge, we must reanimate 
this interest by a vivid representation of the 
paramount dignity of truth and of the lofty 
destination of our intellectual nature. 

3°. In testing the accuracy of our judgments, 
we must be particularly suspicious of those 
results which accord with our private inclina- 
tions and predominant tendencies. 



These rules require no comment. 



^ 



LECTURES ON LOGIC. 109 



LECTURE XXX. 

MODIFIED STOICHEIOLOGY. 
SECTION II. — EREOR — ITS CAUSES AND REMEDIES. 

B. — AS IN THE COGNITIONS, FEELINGS, AND DESIRES. 

II. — WEAKNESS AND DISPROPORTIONED STRENGTH 
OF THE FACULTIES OF KNOWLEDGE. 

I NOW go on to tlie Second Head of the class of Errors lkct. 
founded on the Natural Constitution, the Acquired "''' 



Weakness 



spr 



Habits, and the Reciprocal Relations of our Cognitive anrm 
and Affective Powers, that is, to the Causes of Error ^trength^of 
which originate in the Weakness or Disproportioned J||!; ^r"'' 
Strength of one or more of our Faculties of Knowledge knowledge, 
themselves. 

Here, in the first place, I might consider the errors Neglect of 
which have arisen from the Limited Nature of the Naturnf*^' 
Human Intellect in general, — or rather from the mis- inteiieTr 
takes that have been made by philosophers in denying erroT " 
or not taking this limited nature into account." The 
illustration of this subject is one which is relative to 

a [On this subject see Crusius.] menschlichen Erlcenntniss, § 443, 1st 
[Cliristian August Crusius, Weg ziir ed. 1747. — Ed.] 
Geivissheit unci ZuverldssigJceit der 



110 LECTURES ON LOGIC. 

LECT. and supposes an acquaintance with, some of the ab- 
— ^ — '— strusest speculations in Philosophy, and which belong 
not to Logic, but to Metaphysics, I shall not, therefore, 
do more than simply indicate at present, what it will 
1. Phiio- be proper at another season fully to explain. It is 
Absohuc."" manifest, that, if the human mind be limited, — if it 
only knows as it is conscious, and if it be only con- 
scious, as it is conscious of contrast and opposition, — 
of an ego and non-ego ; — if this supposition, I say, be 
correct, it is evident that those philosophers are in 
error, who virtually assume that the human mind is 
unlimited, that is, that the human mind is capable oi 
a knowledge superior to consciousness, — a cognition 
in which knowledge and existence,' — the Ego and 
non-Ego, — God and the creature, — are identical; that 
is, of an act in which the mind is the Absolute, and 
knows the Absolute. This philosophy, the statement 
of which, as here given, it would require a long com- 
mentary to make you understand, is one which has 
for many years been that dominant in Germany ; it 
is called the Philosophy of the Absolute, or the Phi- 
losophy of Absolute Identity. This system, of which 
Schelling and Hegel are the great representatives, errs 
by denying the limitation of human intelligence with- 
out proof, and by boldly building its edifice on this 
gratuitous negation." 
•2. A one- But thcrc are other forms of philosophy, which err 
ofthefinit- not in actually postulating the infinity of mind, but 
" in taking only a one-sided view of its finitude. It is 
a general fact, which seems, however, to have escaped 
the observation of philosophers, that whatever we can 
positively compass in thought, — whatever we can con- 

a See Discussions, p. 19. — Ed. 



LECTURES ON LOGIC. Ill 

ceive as possible, — in a word, tlie omne coqitahile, lies lect. 

. . XXX 

between two extremes or poles, contradictorily op- L 

posed, and one of which must, consequently, be true, 
but of neither of which repugnant opposites are we 
able to represent to our mind the possibility." To niustrated 

■1 ^ 1^ e ^^' reference 

take one example out oi many : we cannot construe to the two 
to the mind as possible the absolute commencement toHes, -the 
of time ; but we are equally unable to think the j)os- commence- 
sibility of the counter alternative, — its infinite or ab- thrinfiu'^ite 
solute non-commencement, in other words, the infinite mracement, 
regress of time. Now it is evident, that, if we looked '' 
merely at the one of these contradictory opposites and 
argued thus : — whatever is inconceivable is impos- 
sible, the absolute commencement of time is incon- 
ceivable, therefore the absolute commencement ol 
time is impossible ; but, on the principles of Contra- 
diction and Excluded Middle, one or other of two op- 
posite contradictories must be true ; therefore, as the 
absolute commencement of time is impossible, the ab- 
solute or infinite non-commencement of time is neces- 
sary : — I say, it is evident that this reasoning would 
be incompetent and one-sided, because it might be 
converted ; for, by the same one-sided process, the 
opposite conclusion might be drawn in fiivour of the 
absolute commencement of time. 

Now, the unilateral and incompetent reasoning The same 
which I have here supposed in the case of time, is exemlfilLd 
one of which the Necessitarian is guilty, in his argu- Ihe Necessl- 
ment to prove the impossibility of human volitions mentl^a^St 
being free. He correctly lays down, as the founda- V^ihT" "^ 
tion of his reasoning, two propositions which must at wT 
once be allowed : 1°, That the notion of the liberty of 



o See Discussions, p. 601 et seq. et seq. — Ed. 
Lectures on Metaphysics, vol. ii. p. 368 



112 LECTURES ON LOGIC. 



LECT. volition involves tlie supposition of an absolute com- 
^ mencement of volition, that is, of a volition which is 



a cause, but is not itself, qua cause, an effect. 2°, 
That the absolute commencement of volition, or of 
aught else, cannot be conceived, that is, cannot be 
directly or positively thought as possible. So far he is 
correct ; but when he goes on to apply these princi- 
ples by arguing, (and be it observed this syllogism 
lies at the root of all the reasonings for necessity), 
Whatevei' is inconceivable is im2')ossihle ; hut the sup- 
2)osition of the absolute comme7iGeme7it of volition is 
inconceivable ; the7'efore, the supposition of the abso- 
lute coTYimencement of volition {the condition of free 
will) is impossible, — we may here demur to the sump- 
tion, and ask him, — Can he positively conceive the 
opposite contradictory of the absolute commencement, 
that is, an infinite series of relative non-commence- 
ments 1 If he answers, as he must, that he cannot, 
we may again ask him, — By what right he assumed 
as a self-evident axiom for his sumption, the proposi- 
tion, — that ivhatever is inconceivable is impossible, or 
by what right he could subsume his minor premise, 
when by his own confession he allows that the oppo- 
site contradictory of his minor premise, that is, the 
very proposition he is apagogically proving, is, like- 
wise, inconceivable, and, therefore, on the principle of 
his sumption, likewise impossible. 
And in the Thc samc inconsequence would equally apply to 
LfbcrtaHan I'bie Libertarian, who should, attempt to prove that 
i^TehTiftf free-will must be allowed, on the ground, that its 
ree-wiii. QQi-|^^j.r^(ji(}tory opposltc is impossible, because incon- 
ceivable. He cannot prove his thesis by such a pro- 
cess ; in fact, by all speculative reasoning from the 



LECTUEES ON LOGIC. 113 

conditions of thought, the two doctrines are {?i ceqidli- lect. 
hrio; — both are equally possible, — both are equally in- -^ — '— 
conceivable. It is only when the Libertarian descends 
to arguments drawn from the fact of the Moral Law 
and its conditions, that he is able to throw in reasons 
which incline the balance in his favour. 

On these matters I, however, at present only touch, 
in order to show you under what head of Error these 
reasonings would naturally fall. 

Leaving, therefore, or adjourning, the consideration Weakness 
of the imbecility of the human intellect in general, portioned 
I shall now take into view, as a source of logical error, the several 
the Weakness or Disproportioned Strength of the sev- Fatuities, - 
eral Cognitive Faculties. Now, as the Cognitive Fa- knor. 
culties in man consist partly of certain Lower Powers, paSeTof 
which he possesses in common with other sensible ^g^'^owerami 
existences, namely, the Presentative, the Eetentive, the '"^ ^^'s^"'''- 
Eepresentative, and the Eeproductive Faculties, and 
partly of certain Higher Powers, in virtue of which he 
enters into the rank of intelligent existences, namely, 
the Elaborative and Regulative Faculties, — it will be 
proper to consider the powers of these two classes 
severally in succession, in so far as they may afford the 
causes or occasions of error. 

Of the lower class, the first faculty in order is the i. The 
Presentative or Acquisitive Faculty. This, as you ciass,— 
remember, is divided into two, viz. into the faculty sentative 

/» 1 Faculty. 

which presents us with the phpenomena oi the outer 
world, and into the faculty which presents us with the 
phfenomena of the inner." The former is External 
Perception, or External Sense ; the latter is Self-con- 
sciousness, Internal Perception, or Internal Sense. I 

a See Lectures on Metaphysics, vol. ii. p. 23 et seq. — Ed. 
VOL. II. H 



— as a 
source of 
Error. 



lU LECTURES ON LOGIC. 

LECT. commence, therefore, with the Faculty of External 
'— Perception, in relation to which I give you the follow- 
ing paragraph. 

Par.xcvii. '^ XCVII. When aught is presented through the 

PercepTionl outcr scuses, there are two conditions necessary 

for its adequate perception : — 1°, The relative Or- 
gans must be present, and in a condition to dis- 
charge their functions ; and 2°, The Objects them- 
selves must bear a certain relation to these or- 
gans, so that the latter shall be suitably affected, 
and thereby the former suitably apprehended. 
It is possible, therefore, that, partly through the 
altered condition of the organs, partly through 
the altered situation of the objects, dissimilar 
presentations of the same, and similar presenta- 
tions of different, objects, may be the result." 



Expiica- "In the first place, without the organs specially 

Conditions subscrvieut to External Perception, — without the eye, 
adequate ^^^^ ^^^' ^^v scusible perccptious of a precise and de- 
Extefnai**^ terminate character, such, for example, as colour or 
Perception. gQ^JJ(^^ ^yq j^q^ competcut to mau. In the second 
place, to perform their functions, these organs must be 
in a healthy or normal state ; for if this condition be 
not fulfilled, the presentations which they furnish are 
null, incomplete, or false. But, in the third place, 
even if the organs of sense are sound and perfect, the 
objects to be presented and perceived must stand to 
these organs in a certain relation, — must bear to them 
a certain proportion ; for, otherwise, the objects can- 
not be presented at all, or cannot be perceived without 

a Krug, Lof/iJc, gl 38.— Ed. [Cf. p. 273. Bachmann, Lo[/!l; § 407, p. 
Caro, Nourelle Logiquc, part ii. ch. vi. 553.] 



LECTURES ON LOGIC. 115 

illusion. The sounds, for example, which we are to lect. 

XXX. 

hear, must neither be too high nor too low in quality ; — — ^ 
the bodies which we are to see, must neither be too inusLs of 
near nor too distant, — must neither be too feebly nor 
too intensely illuminated. In relation to the second 
condition, there are given, in consequence of the al- 
tered state of the organs, on the one hand, different 
presentations of the same object ; — thus to a person 
who has waxed purblind, his friend appears as an utter 
stranger, the eye now presenting its objects with less 
clearness and distinctness. On the other hand, there 
are given the same, or undistinguishably similar, presen- 
tations of different objects ; — thus to a person in the 
jaundice, all things are presented yellow. In relation 
to the third condition, from the altered position of 
objects, there are, in like manner, determined, on the 
one hand, different presentations of the same objects, 
— as when the stick which appears straight in the air 
appears crooked when partially immersed in water; and, 
on the other hand, identical presentations of different 
objects, as when a man and a horse appear in the dis- 
tance to be so similar, that the one cannot be discrim- 
inated from the other. In all these cases, these illu- 
sions are determined, — illusions which may easily be- 
come the occasions of false judgments."" 

" In regard to the detection of such illusions and Precautions 
obviating the error to which they lead, it behoves us to the detec- 

,._-,-. . -j^-^ . - tion of illu- 

to take the lollowmg precautions. We must, m thesionsof the 
first place, examine the state of the organ. If found obviatmg 

1j16 errors 

defective, we must endeavour to restore it to perfec- to wiiich 
tion, but if this cannot be done, we must ascertain 
the extent and nature of the evil, in order to be upon 

o Krug, Lofjil-, § 138. Anm. — Ed. 



IIG 



LECTURES ON LOGIC. 



LECT. 
XXX. 



our guard in regard to quality and degree of tlie false 
presentation. 

" In tlie second place, we must examine the relative 
situation of the object, and if this be not accommo- 
dated to the organ, we must either obviate the dis- 
proportion and remove the media which occasion the 
illusion, or repeat the observation under different cir- 
cumstances, compare these, and thus obtain the means 
of making an ideal abstraction of the disturbing 
causes." « 

In regard to the other Presentative Faculty, — the 
Faculty of Self-consciousness, — Internal Perception, 
or Internal Sense, as we know less of the material 
conditions which modify its action, we are unable to 
ascertain so precisely the nature of the illusions of 
which it may be the source. In reference to this sub- 
ject you may take the following paragraph. 



Par. XCVIIL 

b. Self- con- 
sciousness, 
— as a 
source of 
Error. 



^ XCVIIL The faculty of Self-consciousness, or 
Internal Sense, is subject to various changes, 
which either modify our apprehensions of ob- 
jects, or influence the manner in which we judge 
concerning them. In so far, therefore, as false 
judgments are thus occasioned. Self-consciousness 
is a source of error,^ 



Explica- 
tion. 
Self- con- 
sciousness 
varies in 
intensity. 



It is a matter of ordinary observation, that the 
vivacity with which we are conscious of the various 
phaenomena of mind, difi'ers not only at different times, 
in different states of health, and in different degrees 
of mental freshness and exhaustion, but, at the same 



a Krug, LofjUc, § 155. — Ed. 



B Krug, LoyU,; § I.IO.— Ed. 



LECTURES ON LOGIC. 117 

time, differs in regard to tlie different kinds of tliese lect. 

. XXX 

phsenomena themselves. According to the greater or 1^- 

less intensity of this faculty, the same thoughts of 
which we are conscious are, at one time, clear and 
distinct, at another, obscure and confused. At one 
time we are almost wholly incapable of reflection, and 
every act of self-attention is forced and irksome, and 
differences the most marked pass unnoticed ; while, 
at another, our self-consciousness is alert, all its appli- 
cations jileasiug, and the most faint and fugitive 
j)h8enomena arrested and observed. On one occasion, 
self-consciousness, as a reflective cognition, is strong ; 
on another, all reflection is extinguished in the inten- 
sity of the direct consciousness of feeling or desire. In 
one state of mind our representations are feeble; in 
another, they are so lively that they are mistaken for 
external realities. Our self-consciousness may thus 
be the occasion of frequent error : for, according to its 
various modifications, we may form the most 0|)posite 
judgments concerning the same things, — pronouncing 
them, for example, now to be agreeable, now to be 
disagreeable, according as our Internal Sense is vari- 
ously affected. 

The next is the Eetentive or Conservative Faculty, 
— Memory strictly so called ; in reference to which I 
give you the following paragraph. 

IF XCIX. Memory, or the Conservative Faculty, Par. xcix. 
is the occasion of Error, both when too weak and -^as a 
when too strong. When too weak, the complement Error. 
of cognitions w^hich it retains is small and indis- 
tinct, and the Understanding or Elaborative 
Faculty is, consequently, unable adequately to 



118 LECTURES ON LOGIC. 

LECT. j^iclg® concerning the similarity and differences 

11- of its representations and concepts. When too 

strong, the Understanding is overwhelmed with 
the multitude of acquired cognitions simultane- 
ously forced upon it, so that it is unable calmly 
and deliberately to compare and discriminate 
these, a 

Expii.a- That both these extremes, — that both the insuffi- 
cient and the superfluous vigour of the Conservative 
Faculty are severally the sources of error, it will not 
require many observations to make apparent. 

FecUc lu regard to a feeble memory, it is manifest that a 

multitude of false judgments must inevitably arise 
from an incapacity in this faculty to preserve the 
observations committed to its keeping. In conse- 
quence of this incapacity, if a cognition be not wholly 
lost, it is lost at least in part, and the circumstances 
of time, place, persons and things confounded with 
each other. For example, — I may recollect the tenor 
of a passage I have read, but from defect of memory 
may attribute to one author what really belongs to 
another. Thus a botanist may judge two difierent 
plants to be identical in species, having forgotten the 
differential characters by which they w^ere discrimin- 
ated ; or he may hold the same plant to be two different 
species, having examined it at different times and 
places.^ 

Strong Though nothiug could be more erroneous than a 

general and unqualified decision, that a great memory 
is incompatible with a sound judgment, yet it is an 
observation confirmed by the experience of all ages 

a [Of. Bachmnnn, Loyik, § iOS.] j8 Krug, Lo^jll; § 141. Anra.— Ed. 



XXX. 



LECTUEES ON LOGIC. 110 

and countries, not only that a great memory is no lect 
condition of high intellectual talent, but that great 
memories are very frequently found in combination 
with comparatively feeble powers of thought." The 
truth seems to be, that where a vigorous memory is 
conjoined with a vigorous intellect, not only does the 
force of the subsidiary faculty not detract from the 
strength of the principal, but, on the contrary, tends 
to confer on it a still higher power ; whereas when 
the inferior faculty is disproportionately strong, that 
so far from nourishing and corroborating the superior, 
it tends to reduce this faculty to a lower level than 
that at which it would have stood, if united with a 
less overj^owering subsidiary. The greater the maga- 
zine of various knowledge which the memory contains, 
the better for the understanding, provided the un- 
derstanding can reduce this various knowledge to 
order and subjection " A great memory is the prin- 
cipal condition of bringing before the mind many 
different representations and notions at once, or in 
rapid succession. This simultaneous or nearly simul- 
taneous presence disturbs, however, the tranquil com- 
parison of a small number of ideas, which, if it shall 
judge aright, the intellect must contemplate with a 
fixed and steady attention." ^ Now, where an intellect 
possesses the power of concentration in a high degree, 
it will not be harassed in its meditations by the ojBS.- 
cious intrusions of the subordinate faculties, however 
vigorous these in themselves may be, but will control 
their vigour by exhausting in its own operations the 



o Compare Lectures on Metaphysics, Muets, quoted by Stewart, Elem., Part 
vol. ii. p. 223. — Ed. iii. ch. i. sect. vi. Collected Works, 

/3 Diderot, Lettre sur Ics Suurcls et vol. iv. p. 249. 



120 LECTUEES ON LOGIC. 

LECT. whole applicable energy of mind. AVliereas where 

'— the inferior is more vigorous than the superior, it will, 

in like manner, engross in its own function the dis- 
posable amount of activity, and overwhelm the prin- 
cipal faculty with materials, many even in proportion 
as it is able to elaborate few. This appears to me the 
reason, why men of strong memories are so often men 
of proportionally weak judgments, and why so many 
errors arise from the possession of a faculty, the per- 
fection of which ought to exempt them from many 
mistaken judgments. 
Remotiics As to thc remedy for these opposite extremes. The 
opposite former, — the imbecility of Memory, — can only be allevi- 
ated by invigorating the capacity of Retention through 
mnemonic exercises and methods ; the latter, — the in- 
ordinate vigour of Memory, — by cultivating the Under- 
standing to the neglect of the Conservative Faculty. 
It will, likewise, be necessary to be upon our guard 
aofainst the errors orio-inatino; in these counter sources. 
In the one case distrusting the accuracy of the facts, 
in the other, the accuracy of their elaboration. * 
3. The Re- The ncxt faculty is the Reproductive. This, when 
Faculty, its Operation is voluntarily exerted, is called Recollec- 
tion or Reminiscence ; when it energises spontane- 
ously or without volition, it is called Suggestion. The 
laws by which it is governed in either case, but espe- 
cially in the latter, are called the Laws of Mental 
Association. This Reproductive Faculty, like the 
Retentive, is the cause of error, both if its vigour be 
defective, or if it be too strong. I shall consider Re- 
collection and Suggestion severally and apart. In 
regard to the former I give you the following para- 
graph. 

a Cf. Ki'ug_, Lvijllc, § 156. Anm. — Ed. 



LECTURES ON LOGIC. 121 

IT C. The Eeproductive Faculty, in so far lect, 



XXX. 



Par. C. 



as it is voluntarily exercised, as Eeminiscence, 
becomes a source of Error as it is either too p . . 

a. Keiniuis- 

sluggish or too prompt, precisely as the Reten- ^^^Ijll^^of 
tive Faculty, combined with which it constitutes ^'■™''- 
Memory in the looser signification. 

It is necessary to say very little in special reference Ex-piica- 
to Reminiscence, for what was said in regard to the Reminis- 
Conservative Faculty or Memory Proper in its higher its undue 
vigour, was applicable to, and in fact supposed a cor- ' 
responding degree of, the Reproductive. For, however 
great may be the mass of cognitions retained in the 
mind, that is, out of consciousness but potentially 
capable of being called into consciousness, these can 
never of themselves oppress the Understanding by 
their simultaneous crowding or rapid succession, if 
the faculty by which they are revoked into conscious- 
ness be inert ; whereas, if this revocative faculty be 
comparatively alert and vigorous, a smaller magazine 
of retained cognitions may suffice to harass the intel- 
lect with a ceaseless supply of materials too profuse 
for its capacity of elaboration. 

On the other hand, the inactivity of our Eecollec- its inani- 
tion is a source of error, precisely as the weakness of ^' ^' 
our Memory proper ; for it is of the same effect in 
relation to our judgments, whether the cognitions re- 
quisite for a decision be not retained in the mind, or 
whether, being retained, they are not recalled into 
consciousness by Reminiscence. 

In regard to Suggestion, or the Reproductive Faculty 
operating spontaneously, that is, not in subservience 
to an act of "Will, — I shall give you the following 
paragraph. 



tion. 



122 LECTURES ON LOGIC. 

LECT. IF CI. As our Coo-nitions, Feelings, and Desires 

XXX 

L are connected together by what are called the 

Par CI. Laws of Associatioii, and as each link in the 

b. ougges- •' 

tion,- as a chain of thought suo-o-ests or awakens into con- 

source of ^ ^^ 

Error. sciousness some other in conformity to these 

Laws, — these Laws, as they bestow a strong sub- 
jective connection on thoughts and objects of a 
wholly arbitrary union, frequently occasion great 
confusion and error in our j adgments. 

Expiica- " Even in methodical thinking, we do not connect 

all our thoughts intentionally and rationally, but 
many press forward into the train, either in conse- 
quence of some external impression, or in virtue of 
certain internal relations, which, however, are not of a 
logical dependency. Thus, thoughts tend to suggest 
each other, which have reference to things of which 
we were previously cognisant as coexistent, or as im- 
mediately consequent, which have been apprehended 
as bearing a resemblance to each other, or which have 
stood together in reciprocal and striking contrast. 
This connection, though precarious and non-logical, is 
thus, however, governed by certain laws, which have 
been called the Laivs of Association" " These laws, 
which I have just enumerated, viz. the Law of Co- 
existence or Simultaneity, the Law of Continuity or 
Immediate Succession, the Law of Similarity, and the 
Law of Contrast, are all only special modifications of 
one general law which I would call the Law of Redin- 
tegration ^ ; that is, the principle according to which 
whatever has previously formed a part of one total 
act of consciousness, tends, when itself recalled into 

a Krug, Zo^//i-, § 144. Anm.— Ed. ii. p. 233 ei: scj. — Eo. 
^ See Lectures on ^Ictajph/jtsics, vol. 



LECTURES OX LOGIC. 123 

consciousness, to reproduce along with it the other lect. 
parts of that original whole. But though these tend- ^ ' ' " 
encies be denominated laivs, the influence which they 
exert, though often strong and sometimes irresistible, 
is only contingent ; for it frequently happens that 
thoughts which have previously stood to each other in 
one or other of the four relations do not suo-o-est each 
other. The Laws of Association stand, therefore, on 
a very different footing from the laws of logical con- 
nection. But those Laws of Association, contingent 
though they be, exert a great and often a very perni- 
cious influence upon thought, inasmuch as by the in- 
voluntary intrusion of representations into the mental 
chain, which are wholly irrelevant to the matter in 
hand, there arises a perplexed and redundant tissue 
of thouglit, into which false characters may easily 
find admission, and in which true characters may 
easily be overlooked.'' But this is not all. For, by 
being once blended together in our consciousness, 
things really distinct in their nature tend again natu- 
rally to reassociate, and, at every repetition of this 
conjunction, this tendency is fortified, and their mu- 
tual suggestion rendered more certain and irresistible. 

It is in virtue of this principle of Association and influence 
Custom, that things are clothed by us with the preca- ation in 
rious attributes of deformity or beauty ; and some Taste, 
philosophers have gone so far as to maintain that our 
principles of Taste are exclusively dependent on the 
accidents of Association. But if this be an exagger- 
ation, it is impossible to deny that Association en- 
joys an extensive jurisdiction in the empire of taste, 
and, in particular, that fashion is almost wholly sub- 
ject to its control. 

o Kriig, Lofjil, § 14-1. Aum.— Ed. 



124 LECTURES ON LOGIC. 



LECT. On tliis subject I may quote a few sentences from 



XXX 



- the first volume of Mr Stewart's Elements. " In mat- 
quoted' ters of Taste, the effects which we consider, are pro- 
duced on the mind itself, and are accompanied either 
with pleasure or with pain. Hence the tendency to 
casual association is much stronger than it commonly 
is with respect to physical events ; and when such 
associations are once formed, as they do not lead to 
any important inconvenience, similar to those which 
result from physical mistakes, they are not so likely 
to be corrected by mere experience, unassisted l)y 
study. To this it is owing that the influence of asso- 
ciation on our judgments concerning beauty and de- 
formity, is still more remarkable than on our specula- 
tive conclusions ; a circumstance wdiich has led some 
philosophers to suppose that association is sufficient 
to account for the origin of these notions, and that 
there is no such thing as a standard of taste, founded 
on the principles of the human constitution. But this 
is undoubtedly pushing the theory a great deal too 
far. The association of ideas can never account for 
the origin of a new notion, or of a joleasure essentially 
different from all the others which we know. It may, 
indeed, enable us to conceive how a thing indifferent 
in itself may become a source of pleasure, by being 
connected in the mind with something else which is 
naturally agreeable ; but it presupposes, in every in- 
stance, the existence of those notions and those feel- 
ings which it is its province to combine : insomuch 
that, I apprehend, it will be found, wherever associa- 
tion produces a change in our judgments on matters 
of taste, it does so by co-operating with some natural 
principle of the mind, and implies the existence of 
certain original sources of pleasure and uneasiness. 



LECTUKES ON LOGIC. 125 

" A mode of dress, wliicli at first appeared awk- lect, 

ward, acquires, in a few weeks or months, the appear- 

ance of elegance. By being accustomed to see it 
worn by those whom we consider as models of taste, 
it becomes associated with the agreeable impressions 
which we receive from the ease and grace and refine- 
ment of their manners. When it pleases by itself, the 
efiect is to be ascribed, not to the object actually be- 
fore us, but to the impressions with w^hich it has been 
generally connected, and which it naturally recalls to 
the mind. 

" This observation points out the cause of the per- 
petual vicissitudes in dress, and in everything whose 
chief recommendation arises from fashion. It is evi- 
dent that, as far as the agreeable effect of an ornament 
arises from association, the effect will continue only 
while it is confined to the higher orders. When it is 
adopted by the multitude, it not only ceases to be 
associated with ideas of taste and refinement, but it is 
associated with ideas of affectation, absurd imitation, 
and vulgarity. It is accordingly laid aside by the 
higher orders, who studiously avoid every cii^cum- 
stance in external appearance which is debased by low 
and common use ; and they are led to exercise their 
invention in the introduction of some new peculiari- 
ties, which first become fashionable, then common, and 
last of all, are abandoned as vulgar." "* 

" Our moral judgments, too, may be modified, and 
even perverted to a certain degree, in consequence of 
the operation of the same principle. In the same 
manner in which a person who is regarded as a model 
of taste may introduce, by his example, an absurd or 
fantastical dress ; so a man of splendid virtues may 

a Elements, vol. i., Part i. chap. v. Collected Worl-s, ii. p. 3"22 et scq. 



126 LECTURES ON LOGIC. 

LECT. attract some esteem also to his imperfections ; and, if 

'— placed in a conspicuous situation, may render his vices 

and follies objects of general imitation among the 
multitude. 

" ' In the reign of Charles II.,' says Mr Smith," ' a 
degree of licentiousness was deemed the characteris- 
tic of a liberal education. It was connected, according 
to the notions of those times, with generosity, sincer- 
ity, magnanimity, loyalty ; and proved that the per- 
son who acted in this manner was a gentleman, and 
not a puritan. Severity of manners and regularity 
of conduct, on the other hand, were altogether un- 
fashionable, and were connected, in the imagination of 
that age, with cant, cunning, hypocrisy, and low man- 
ners. To superficial minds the vices of the great seem 
at all times agreeable. They connect them not only 
with the splendour of fortune, but with many superior 
virtues which they ascribe to their superiors ; with the 
spirit of freedom and independency ; with frankness, 
generosity, humanity, and politeness. The virtues of 
the inferior ranks of people, on the contrary, — their 
parsimonious frugality, their painful industry, and 
rigid adherence to rules, seem to them mean and dis- 
agreeable. They connect them both with the mean- 
ness of the station to which these qualities commonly 
belong, and with many great vices which they suppose 
usually accompany them ; such as an abject, cowardly, 
ill-natured, lying, pilfering disposition.' "^ 
Condiiiac " In general," says Condillac, " the impression we 
the influ^ experience in the different circumstances of life, makes 
Ab^sodation. US assoclatc ideas with a force which renders them 
ever after for us indissoluble. We cannot, for ex- 

o Thcorii of Moral Sentivients, P Elements, vol. i. c. v. § 3. Col- 
Piirt V. c. 2. — Ed. lecfed Works, vol. ii. p. 335. 



LECTURES ON LOGIC. 127 

ample, frequent tlie society of our fellow-men without lect. 
insensibly associating the notions of certain intellec- ' ' ^ ' 
tual or moral qualities with certain corporeal charac- 
ters. This is the reason why persons of a decided 
physiognomy please or displease us more than others ; 
for a physiognomy is only an assemblage of characters, 
with which we have associated notions which are not 
suggested without an accompaniment of satisfaction 
or disgust. It is not, therefore, to be marvelled at that 
we judge men according to their physiognomy, and 
that we sometimes feel towards them at first sight 
aversion or inclination. In consequence of these 
associations, we are often vehemently prepossessed in 
favour of certain individuals, and no less violently 
disposed against others. It is because all that strikes 
us in our friends or in our enemies is associated with 
the ao-reeable or the disa2;reeable feelino; which we 
severally experience ; and because the faults of the 
former borrow always something pleasing from their 
amiable qualities ; whereas the amiable qualities of 
the latter seem always to participate of their vices. 
Hence it is that these associations exert a powerful 
influence on our whole conduct. They foster our love 
or hatred ; enhance our esteem or contempt ; excite 
our gratitude or indignation ; and produce those sym- 
pathies, — those antipathies, or those capricious inclin- 
ations, for which we are sometimes sorely puzzled to 
render a reason. Descartes tells us that through life 
he had always felt a strong predilection for squint 
eyes, — which he explains by the circumstance, that 
the nursery-maid by whom he had been kindly tended, 
and to whom as a child he was, consequently, much 
attached, had this defect." '^ 'S Gravesande, I think it 

o Oviijlne d:s Connohsances Ilumalnes, sect. ii. ch. ix. § SO. — Ed. 



128 LECTURES ON LOGIC. 

LECT. is, who tells us lie knew a man, and a man otherwise 

^ L of sense, who had a severe fall from a waggon ; and 

thereafter he could never enter a waggon without fear 
and trembling, though he daily used, without appre- 
hension, another and far more dangerous vehicle." A 
girl once and again sees her mother or maid fainting 
and vociferating at the appearance of a mouse ; if she 
has afterwards to escajDC from danger, she will rather 
pass through flames than take a patent way, if ob- 
structed by a ridiculiis miis. A remarkable example 
of the false judgments arising from this principle of 
association, is recorded by Herodotus and Justin, in 
reference to the war of the Scythians with their slaves. 
The slaves, after they had repeatedly repulsed several 
attacks with arms, were incontinently put to flight 
when their masters came out against them with their 
whips.'^ 

I shall now ofi'er an observation in regard to the 
appropriate remedy for this evil influence of Associa- 
tion. 
Only re- The ouly uicau by which we can become aware of, 

"he influence couutcract, aud overcome, this besetting v/eakness of 
tioni^rtile our nature, is Philosophy, — the PhilosojDhy of the 
of"he^"'"^ Human Mind ; and this studied both in the conscious- 
MhiX" ness of the individual, and in the history of the spe- 



cies. The philosophy of mind, as studied in the con- 
sciousness of the individual, exhibits to us the source 
and nature of the illusion. It accustoms us to discri- 
minate the casual, from the necessary, combinations 
of thought ; it sharpens and corroborates our facul- 

a Tntroductio ad Philosopliiam, Lo- low are also from 'S Gravesaiide. — 

yica, c. 26. The example, however, is Ed. 

given as a supposed case, not as a ^ Herod., iv. 3. Justin., ii. 5 

fact. The two instances which fol- Ed. 



LECTURES ON LOGIC. 129 

ties, encourages our reason to revolt asfainst the blind lect. 

. . . XXX. 

preformations of opinion, and finally enables us to '- 

break through the enchanted circle mthin which Cus- 
tom and Association had enclosed us. But in the 
accomplishment of this end, we are greatly aided by 
the study of man under the various circumstances 
which have concurred in modifying his intellectual 
and moral character. In the great spectacle of his- 
tory, we behold in different ages and countries the 
predominance of different systems of association, and 
these ages and countries are, consequently, distin- 
guished by the prevalence of different systems of 
opinions. But all is not fluctuating ; and, amid the 
ceaseless changes of accidental circumstances and pre- 
carious beliefs, we behold some principles ever active, 
and some truths always commanding a recognition. 
We thus obtain the means of discriminating, in so 
far as our unassisted reason is conversant about mere 
worldly concerns, between what is of universal and 
necessary certainty, and what is only of local and 
temporary acceptation ; and, in reference to the latter, 
in witnessing the influence of an arbitrary association 
in imposing the most irrational opinions on our fel- 
low men, our eyes are opened, and we are warned of 
the danger from the same illusion to ourselves. And 
as the philosophy of man affords us at once the indi- 
cation and the remedy of this illusion, so the philo- 
sophy of man does this exclusively and alone. Our 
irrational associations, our habits of groundless credu- 
lity and of arbitrary scepticism, find no medicine in 
the study of aught beyond the domain of mind itself. 
As Goethe has well observed, " Mathematics remove 
no prejudice ; they cannot mitigate obstinacy, or 

i VOL. II. I 



130 LECTUEES ON LOGIC. 

LECT. temper party-spirit ;"« in a word, as to any moral 



XXX. 



influence upon the mind they are absolutely null. 
Hence we may well explain the aversion of Socrates 
for these studies, if carried beyond a very limited 
extent. 
The Repre- The ncxt faculty in order is the Eepresentative, or 

sentative -^ . . ..- .., 

Faculty, Imamnatiou proper, which consists in the OTeater or less 

or Imagiua- pit • t • •iti 

tion Proper, power of lioldiug up an ideal object in the light of 
consciousness. The energy of Representation, though 
dependent on Retention and Reproduction, is not to 
be identified with these operations. For though these 
three functions (I mean Retention, Reproduction, and 
Representation), immediately suppose, and are immedi- 
ately dependent on, each other, they are still mani- 
festly discriminated as different qualities of mind, in- 
asmuch as they stand to each other in no determinate 
proportion. We find, for example, in some indivi- 
duals the capacity of Retention strong, but the Re- 
productive and Representative Faculties sluggish and 
weak. In others, again, the Conservative tenacity is 
feeble, but the Reproductive and Representative ener- 
gies prompt and vivid ; while in others the power of 
Reproduction may be vigorous, but what is recalled is 
never pictured in a clear and distinct consciousness. 
It will be generally, indeed, admitted, that a strong re- 
tentive memory does not infer a prompt recollection ; 
and still more, that a strong memory and a prompt 
recollection do not infer a vivid imagination. These, 
therefore, though variously confounded by philoso- 
phers, we are warranted, I think, in viewing as elemen- 
tary qualities of mind, which ought to be theoretically 
distinguished. Limiting, therefore, the term Imagina- 

a Wei-Jce, xxii. p. 258. Quoted by Scheidler, Psycliolorjic, p. 146. 



LECTURES ON LOGIC. 131 

tion to the mere Faculty of Representing in a more or lect. 
less vivacious manner an ideal object, — this Faculty ' ' ^ ' 
is the source of errors which I shall comprise in the 
following paragraph. 

% CII. Imagination, or the Faculty of Repre- Par. cii. 

. -, -, . . ,, , , 4. Imagina- 

sentmg with more or less vivacity a recalled ob- tion, —as a 

„ ... 1 p -n 11 source of 

ject 01 cognition, is the source ot Horrors, both Error. 
when it is too languid and when it is too vio;or- 
ous. In the former case, the object is represent- 
ed obscurely and indistinctly ; in the latter, the 
ideal representation affords the illusive appear- 
ance of a sensible presentation. 

A strong imagination, that is, the power of holding Expiica- 
up any ideal object to the mind in clear and steady Necessity 
colours, is a faculty necessary to the poet and to the tion in" 
artist ; but not to them alone. It is almost equally pursuits. 
requisite for the successful cultivation of every scien- 
tific pursuit ; and, though differently applied, and 
different in the character of its representations, it 
may well be doubted whether Aristotle did not pos- 
sess as powerful an imagination as Homer. The 
vigour and perfection of this faculty is seen, not so 
much in the representation of individual objects and 
fragmentary sciences, as in the representation of sys- 
tems. In the better ages of antiquity the perfection, Diverse 
— the beauty, of all works of taste, whether in Poetry, Lticsof Art 
Eloquence, Sculpture, Painting, or Music, was princi- Lnd modem 
pally estimated from the symmetry or proportion of ""''''■ 
all the parts to each other, and to the whole which 
they together constituted ; and it was only in subser- 
vience to this general harmony that the beauty of the 
several parts was appreciated. In the criticism of 



132 LECTURES ON LOGIC. 

LECT. modern times, on the contrary, tlie reverse is true ; 
'— and we are disposed to look more to the obtrusive qua- 
lities of details than to the keeping and unison of a 
whole. Our works of art are, in general, like kinds 
of assorted patch-work ; — not systems of parts all 
subdued in conformity to one ideal totality, but co- 
ordinations of independent fragments, among which 
a "pz^7'pwci^5 2^cmni(s" seldom comes amiss. The rea- 
son of this difference in taste seems to be, what at first 
sight may seem the reverse, that in antiquity not the 
Reason but the Imagination was the more vigorous ; — 
that the Imagination was able to represent simultane- 
ously a more comprehensive system ; and thus the 
several parts being regarded and valued only as con- 
ducive to the general result, — these parts never ob- 
tained that individual importance, which would have 
fallen to them had they been only created, and only 
considered, for themselves. Now this power of repre- 
senting to the mind a complex system in all its bear- 
ings, is not less requisite to the philosopher than to 
the poet, though the representation be different in 
kind ; and the nature of the philosophic representa- 
tions, as not concrete and palpable like the poetical, 
supposes a more arduous operation, and, therefore, 
even a more vigorous faculty. But Imagination, in 
the one case and in the other, requires in proportion 
to its own power a powerful intellect ; for imagina- 
tion is not poetry nor philosophy, but only the condi- 
tion of the one and of the other. 
Errors But to speak now of the Errors which arise from 
from the"" the disproportion between the Imagination and the 
dispropor- j^(;jgj3^gjjl^ . — ii^Qj originate either in the weakness, or 

gTuatiou"and in tho iuordinatc strength, of the former. 

Judgment. j^^ regard to the errors which arise from the imbe- 



LECTURES ON LOGIC. 133 



cility of tlie Representative Faculty, it is not difficult lect. 
to conceive how this imbecility may become a cause ^^ ^' 



of erroneous judgment. The Elaborative Faculty, in jn'^f^^^'the 
order to judge, requires an object, — requires certain o7ima^lna- 
differences to be given. Now, if the imagination be *''''^- 
weak and languid, the objects represented by it will 
be given in such confusion and obscurity, that their 
differences are either null or evanescent, and judgment 
thus rendered either impossible, or possible only with 
the probability of error. In these circumstances, to 
secure itself from failure, the intellect must not at- 
tempt to rise above the actual presentations of sense ; 
it must not attempt any ideal analysis or synthesis, — 
it must abandon all free and self-active elaboration, 
and all hope of a successful cultivation of knowledge. 

Again, in regard to the opposite errors, those arising prom its 
from the disproportioned vivacity of imagination, — t'oS*"" 
these are equally apparent. In this case the renewed '"''^^'y- 
or newly-modified representations make an equal im- 
pression on the mind as the original presentations, 
and are, consequently, liable to be mistaken for these. 
Even during the perception of real objects, a too lively 
imagination mingles itself with the observation, which 
it thus corrupts and falsifies. Thus arises what is 
logically called the vitimn suhreptionis."' This is fre- 
quently seen in those pretended observations made by 
theorists in support of their hypotheses, in which, if 
even the possibility be left for imagination to inter- 
fere, imagination is sure to fiU up all that the senses 
may leave vacant. In this case the observers are at 
once dupes and deceivers, in the words of Tacitus 
" Fingunt simul creduntque." ^ 

a Krug, Lorjik, § 142. Anm.— Ed. on Metaphysics, vol. i. p. 76.— Ed. 
/8 Hist. lib. ii, c. 8. See Lectures 



134 



LECTURES ON LOGIC. 



LECT. 
XXX. 

Remedies 
for these 
defects of 
the Imagin- 
ation. 



In reirard to tlie remedies for these defects of tlie 
Eepresentative Faculty ; — in the former case, the only 
alleviation that can be proposed for a feeble Imagina- 
tion, is to animate it by the contemplation and study 
of those works of art which are the products of a strong 
Phantasy, and which tend to awaken in the student a 
corresponding energy of that faculty. On the other 
hand, a too powerful imagination is to be quelled and 
regulated by abstract thinking, and the study of phi- 
losophical, perhaps of mathematical, science." 

The faculty which next follows, is the Elaborative 
Faculty, Comparison, or the Faculty of Relations. 
This is the Understanding, in its three functions of 
Conception, Judgment, and Eeasoning. On this fa- 
culty take the following paragraph. 



Par. cm. 

5. Elabor- 
ative Fa- 
culty, — as 
a source of 
Error, 



H cm. The Affections and the Lower Cog- 
nitive Faculties afford the sources and occasions 
of error ; but it is the Elaborative Faculty, Un- 
derstanding, Comparison, or Judgment, which 
truly errs. This faculty does not, however, err 
from strength or over-activity, but from inac- 
tion ; and this inaction arises either from natural 
weakness, from want of exercise, or from the im- 
potence of attention. ^ 



Explica- 
tion. 

Error does 
not lie in 
tlie condi- 
tions of our 
Higher 
Faculties, 
but is pos- 



I formerly observed that error does not lie in the 
conditions of our higher faculties themselves, and that 
these faculties are not, by their own laws, determined 
to false judgments or conclusions : — 

" Nam ueque decipitur ratio, uec deciiDit unquam." y 



a Cf. Krug, Lor/ik, § 156. Anm. — Fries, Loyifc, § 108. Bachmanu, Zo*///;, 
Ed. §411.] 

/3 Krug, Lofj'ik, § 148. — Ed. [Cf. y See above, vol. ii. p. 77.— Ed. 



LECTURES ON LOGIC. 135 

If this were otherwdse, all knowledge would be impos- lect. 
sible, — tlie root of our nature would be a lie. "But 



in the application of the laws of our higher faculties application 
to determinate cases, many errors are possible ; and l\ thosl"^^^^ 
these errors may actually be occasioned by a variety ietelmTnate 
of circumstances. Thus, it is a law of our intelligence, '"'^''^* 
that no event, no phenomenon, can be thought as 
absolutely beginning to be ; we cannot but think that 
all its constituent elements had a virtual existence 
prior to their concurrence, to necessitate its manifest- 
ation to us ; we are thus unable to accord to it more 
than a relative commencement, in other words, we 
are constrained to look upon it as the effect of ante- 
cedent causes. Now though the law itself of our in- 
telligence, — that a cause there is for every event, — be 
altogether exempt from error, yet in the application 
of this law to individual cases, that is, in the attribu- 
tion of determinate causes to determinate effects, we 
are easily liable to go wrong. For we do not know, 
except from experience and induction, what particular 
antecedents are the causes of particular consequents ; 
and if our knowledge of this relation be imperfectly 
generalised, or if we extend it by a false analogy to 
cases not included within our observation, error is 
the inevitable consequence. But in all this there is 
no fault, no failure, of intelligence, there is only a de- 
ficiency, — a deficiency in the activity of intelligence, 
while the Will determines us to a decision before the 
Understanding has become fully conscious of certainty. 
The defective action of the Understanding may arise Defective 
from three causes. In the first place, the faculty of the Under- 
Judgment may by nature be too feeble. This is the may arise 
case in idiots and weak persons. In the second place, causes. 
though not by nature incompetent to judge, the in- feebleness. 



136 



LECTURES ON LOGIC. 



LECT. tellect may bo without the necessary experience, — 

L may not possess the grounds on which a correct judg- 

nocelsTry"^ mcut must bc fouudcd. In the third place, and this 
experience, 'g ^^^ most frcquent cause of error, the failure of the 

c. Incom- -■■ 

petency of uuderstandino; is from the incompetency of that act of 

attention. _ _ ^ , ■■■ '' ^ ^ 

will which is called Atte^itioii. Attention is the vol- 
untary direction of the mind upon an object, with the 
intention of fully apprehending it. The cognitive 
energy is thus, as it were, concentrated upon a single 
point. We, therefore, say that the mind collects itself, 
when it begins to be attentive ; on the contrary, that 
it is distracted, when its attention is not turned upon 
an object as it ought to be. This fixing — this con- 
centration, of the mind upon an object can only be 
carried to a certain degree, and continued for a certain 
time. This degree and this continuance are both de- 
pendent upon bodily circumstances ; and they are 
also frequently interrupted or suspended by the intru- 
sion of certain collateral objects, which are forced upon 
the mind, either from without, by a strong and sudden 
impression upon the senses, or from within, through 
the influence of Association ; and these, when once 
obtruded, gradually or at once divert the attention 
from the original and principal object. If we are not 
sufficiently attentive, or if the eflbrt which accompanies 
the concentration of the mind upon a single object be 
irksome, there arises hurry and thoughtlessness in 
judging, inasmuch as we judge either before we have 
fully sought out the grounds on which our decision 
ought to proceed, or have competently examined their 
validity and effect. It is hence manifest that a multi- 
tude of errors is the inevitable consequence." « 



a Krug, Lofjik, § 148. Aurn. lu aomo places slightly changed. — Ed. 



LECTURES ON LOGIC. 137 

In regard to the Eegulative Faculty, — Common lect. 
Sense, — Intelligence, — vovs, — this is not in itself a ^ ^ ^ ' 



source of error. Errors may, however, arise either from JiVe^Fl!^''' 
overlooking the laws or necessary principles which it "f^^] 



not 
properly a 



source 
Error. 



of 



does contain ; or by attributing to it, as necessary 
and original data, what are only contingent general- 
isations from experience, and, consequently, make no 
part of its complement of native truths. But these 
errors, it is evident, are not to be attributed to the Ee- 
gulating Faculty itself, which is only a place or source 
of principles, but to the imperfect operations of the 
Understanding and Self-consciousness, in not pro- 
perly observing and sifting the phsenomena which it 
reveals. 

Besides these sources of Error, which immediately Remote 
originate in the several powers and faculties of mind, Erroi^in'the 
there are others of a remoter origin arising from the habits de- 
different habits which are determined by the differ- sex"'age, ^ 
ences of sex,« of age,^ of bodily constitution,'^ of stuutlonr' 

-I , • /» inn, n c • /»• education, 

education, oi rank, oi lortune, oi profession, of m- ice 
tellectual pursuit. Of these, however, it is impossible 
at present to attempt an analysis ; and I shall only 
endeavour to afford you a few specimens, and to refer 
you for information in regard to the others to the best 
sources. 

Intellectual pursuits or favourite studies, inasmuch s^eiecte.i 
as these determine the mind to a one-sided cultiva- of Tcse'" 
tion, that is, to the neglect of some, and to the dis- cultivation 
proportioned development of other, of its faculties, are teiiectuai 
among the most remarkable causes of error. This ^'°''®^^' 

a [See Stewart, Elements, vol. iii. Crousaz, Logiquc, t. i. part i. sect. i. 

part iii. sect. v. chap. i. Worls, vol. ch. v. § 15, p. 104.] 

iv. p. 238 et seq.] y [See Crousaz, Lorjique, t. i. p. i. 

/3 [Aristotle, Bliet., L. ii. c. 12. sect. i. ch. v. p. 91 et seq.l 



138 



LECTURES ON LOGIC. 



LECT. 
XXX. 

This ex- 
emplified 
in three 
different 
phases. 
Exclusive 
cultivation. 
1. Of the 
powers of 
Observa- 
tion. 



2. Of Meta- 
physics. 

3. Of Man 
thematics. 



Stewart 
referred to. 



partial or one-sided cultivation is exemplified in three 
different phases. The first of these is shown in the 
exclusive cultivation of the powers of Observation, to 
the neglect of the higher faculties of the Understand- 
ing. Of this type are your men of physical science. 
In this department of knowledge there is chiefly de- 
manded a patient habit of attention to details, in 
order to detect phtenomena, and, these discovered, 
their generalisation is usually so easy that there is 
little exercise afibrded to the higher energies of Judg- 
ment and Reasonino;. It was Bacon's boast that In- 
duction, as applied to nature, would equalise all tal- 
ents, level the aristocracy of genius, accomplish mar- 
vels by co-operation and method, and leave little to 
be done by the force of individual intellects. This 
boast has been fulfilled ; Science has, by the Induc- 
tive Process, been brought down to minds, who pre- 
viously would have been incompetent for its cultiva- 
tion, and physical knowledge now usefully occupies 
many who would otherwise have been without any 
rational pursuit. But the exclusive devotion to such 
studies, if not combined with higher and graver specu- 
lations, tends to wean the student from the more 
vigorous efibrts of mind, which, though unamusing 
and even irksome at the commencement, tend, how- 
ever, to invigorate his nobler powers, and to prepare 
him for the final fruition of the highest happiness of 
his intellectual nature. 

A partial cultivation of the intellect, opposite to 
this, is given in the exclusive cultivation of Meta- 
physics and of Mathematics. On this subject I may 
refer you to some observations of Mr Stewart, in two 
chapters entitled The Metaphysician and The Mathe- 



LECTURES ON LOGIC. 139 

matician, in the third volume of his Elements of the lect. 
Philosophy of the Human Mind, — chapters clistin- -^^^' 
guished equally by their candour and their depth of 
observation. On this subject Mr Stewart's authority 
is of the highest, inasmuch as he was distinguished in 
both the departments of knowledge, the tendency of 
which he so well develops. 



140 



LECTURES ON LOGIC. 



LECTURE XXXI. 



MODIFIED STOICHEIOLOGY. 



SECTION II. — ERROR, — ITS CAUSES AND REMEDIES. 



C. LANGUAGE — D. OBJECTS OF KNOWLEDGE. 



LECT. 
XXXI. 

III. Lan- 
guage, — as 
a source of 
Error. 



Has mail 
invented 
Language r 
Ambiguity 
of the 
question. 



In what 
sense Lan- 
guage is 
natural to 



In my last Lecture, I concluded the survey of the 
Errors which have their origin in the conditions and 
circumstances of the several Cognitive Faculties, and 
now proceed to that source of false judgment, which 
lies in the imperfection of the Instrument of Thought 
and Communication, — I mean Language. 

Much controversy has arisen in regard to the ques- 
tion, — Has man invented Language "? But the differ- 
ences of opinion have in a great measure arisen from 
the ambiguity or complexity of the terms, in which 
the problem has been stated. By language we may 
mean either the power which man possesses of associ- 
ating his thought with signs, or the particular systems 
of signs with which different portions of mankind 
have actually so associated their thoughts. 

Taking language in the former sense, it is a natural 
faculty, an original tendency of mind, and, in this 
view, man has no more invented language than he 
has invented thought. In fact, the power of thought 
and the power of language are equally entitled to be 



LECTURES ON LOGIC. 141 

considered as elementary qualities of intelligence ; for lect. 
while tliey are so different that they cannot be identi- ' ^ ^ ' 
fied, they are still so reciprocally necessary that the 
one cannot exist without the other. It is true, in- 
deed, that presentations and representations of given 
individual objects might have taken place, although 
there were no signs with which they were mentally 
connected, and by which they could be overtly ex- 
pressed ; but all complex and factitious constructions 
out of these given individual objects, in other words, 
all notions, concepts, general ideas, or thoughts proper, 
would have been impossible without an association to 
certain signs, by which their scattered elements might 
be combined in unity, and their vague and evanescent 
existence obtain a kind of definite and fixed and 
palpable reality. Speech and cogitation are thus the 
relative conditions of each other's activity, and both 
concur to the accomj^lisliment of the same joint result. 
The Faculty of Thinking, — the Faculty of forming 
General Notions, — being given, this necessarily tends to 
energy, but the energy of thinking depends upon the 
coactivity of the Faculty of Speech, which itself tends 
equally to energy. These faculties, — these tendencies, 
— these energies, thus coexist and have always co- 
existed ; and the result of their combined action is 
thought in language, and language in thought. So 
much for the origin of Language, considered in general 
as a faculty. 

But, though the Faculty of Speech be natural and wasti.e 

1 . . « . . first lan- 

necessary, that its manitestations are to a certam ex- guage, 
tent contingent and artificial, is evident from the spoken, 
simple fact, that there are more than a single language tion of man 



or au in- 



actually spoken. It may, therefore, be asked, — Was the spiration of 
first language, actually spoken, the invention of man, "^ ''' ^ ' 



142 



LECTURES ON LOGIC. 



LECT. 
XXXI. 

The Latter 
hypothesis 
cousidered. 



Difficulty 
of the 
question. 



Language 
has a gen- 
eral and a 
special 
character. 



or an inspiration of the Deity 1 The latter hypothesis 
cuts, but does not loose, the knot. It declares that 
ordinary causes and the laws of nature are insufficient 
to explain the phcenomenon, but it does not' prove 
this insufficiency ; it thus violates the rule of Parci- 
mony, by postulating a second and hypothetical cause 
to explain an effect, which it is not shown cannot be 
accounted for without this violent assumption. The 
first and greatest difficulty in the question is thus : — 
It is necessary to think in order to invent a language, 
and the invention of a language is necessary in order 
to think ; for we cannot think without notions, and 
notions are only fixed by words." This can only be 
solved, as I have said, by the natural attraction be- 
tween thought and speech, — by their secret affinity, 
which is such that they suggest and, pari ixissu, 
accompany each other. And in regard to the ques- 
tion, — Why, if speech be a natural faculty, it does not 
manifest itself like other natural principles in a uniform 
manner, — it may be answered that the Faculty of 
Speech is controlled and modified in its exercise by 
external circumstances, in consequence of which, 
though its exertion be natural and necessary, and, 
therefore, identical in all men, the special forms of 

decree conventional and 



its exertion are m a 



great 



contingent, and, therefore, different among different 
portions of mankind. 

Considered on one side, languages are the results of 
our intellio:ence and its immutable laws. In conse- 
quence of this, they exhibit in their progress and de- 



o See Rousseau, Discours sur V Ori- prendre Ji penser, ils out eu bien plus 

gine de rhiegalite iMrmi les Ilommes. besoin encore de savoir penser pour 

Premiere Partie. " Si les hommes trouver I'art de la parole." — Ed. 
out eu besoin de la parole pour ap- 



LECTURES ON LOGIC. 1^3 

velopment resemblances and common characters which lect. 

• • X\XI 

allow us to compare and to recall them to certain pri- " " ' ' 
mitive and essential forms, — to evolve a system of 
Universal Grammar. Considered on another side, each 
language is the offspring of particular wants, of special 
circumstances, physical and moral, and of chance. 
Hence it is that every language has particular forms 
as it has peculiar words. Language thus bears the 
impress of human intelligence only in its general 
outlines. There is, therefore, to be found reason and 
philosophy in all languages, but w^e should be wrong 
in believing that reason and philosophy have, in any 
language, determined everything. No tongue, how per- No lau- 
fect soever it may appear, is a complete and perfect perfect 
mstrument oi human thought, rrom its very condi- of thought, 
tions every language must be imperfect. The human 
memory can only compass a limited complement of 
words, but the data of sense, and still more the com- 
binations of the understanding, are wholly unlimited 
in number. No language can, therefore, be adequate 
to the ends for which it exists ; all are imperfect, but 
some are far less incompetent instruments than others. 
From what has now been said, you will be pre- 
pared to find in Language one of the principal sources 
of Error ; but before I go on to consider the particular 
modes in which the Imperfections of Language are the 
causes of false judgments, — I shall comprise the gen- 
eral doctrine in the following paragraph. 

H CIV. As the human mind necessarily re- Par. civ. 
quires the aid of signs to elaborate, to fix, and — Ts^"*^'' 
to communicate its notions, and as Articulate Error. 
Sounds are the species of signs which most 
effectually afford this aid, Speech is, therefore, an 



144 LECTURES ON LOGIC. 

LECT. indispensable instrument in the hio;lier functions 

XXXI 

. — 1-!- of thought and knowledge. But as speech is a 

necessary, but not a perfect, instrument ; its 
imperfection must react upon the mind. For the 
Multitude of Languages, the Difficulty of their 
Acquisition, their necessary Inadequacy, and the 
consequent Ambiguity of Words, both singly 
and in combination, — these are all copious sources 
of Illusion and Error.« 

Expiica- We have already sufficiently considered the reason 
Sign's neces- why tliouglit is dependent upon some system of signs 
internal or symbols, both for its internal perfection and ex- 
of Thought, ternal expression./^ The analyses and syntheses, — the 
decompositions and compositions, — in a word, the ela- 
borations, performed by the Understanding upon the 
objects presented by External Perception and Self- 
Consciousness, and represented by Imagination, — 
these operations are faint and fugitive, and would have 
no existence, even for the conscious mind, beyond the 
moment of present consciousness, were we not able to 
connect, to ratify, and to fix them, by giving to their 
parts, (which would otherwise immediately faU asun- 
der), a permanent unity, by associating them with a 
sensible symbol, which we may always recall at plea- 
sure, and which, when recalled, recalls along with it 
the characters which concur in constituting a notion 
or factitious object of intelligence. So far signs are 
necessary for the internal operation of thought itself. 

aKrug, Logik,%li5. — Ed. [Of. Er- §109. Caro, Logique, Part. i. ch. i. 

nesti,JnitiaI)octri7iceSolicUoris: Pars art. 9, p. 121. Crousaz, Toussaint.] 

Altera; Dialectica, c. 2,% 2i. Wytten- [Crousaz, Logique, t. iii. part i. sect. 

bach, Prwcejita Phil. Log. P. iii. c. iii. iii. c. 2, p. 68 et seq. Toussaint, De la 

p. 98. Tittel, Logik, p. 292. Kirwaii, Pcnscc. Chs. viii. x. Ed.] 

Logick, i. 214. Fiiea, Si/st,an der Logik, ^ See above, vol. i. p. 137. — Ed. 



LECTUKES ON LOGIC. 145 

But for the communication, of tliouo-ht from one mind lect. 

XXXI. 

to another, signs are equally indispensable. For in ' ' ' 



itself thought is known, — thought is knowable, onlyihe'com- 
to the thinking mind itself ; and were we not enabled orxhoigTit. 
to connect certain complements of thought to certain 
sensible symbols, and by their means to suggest in 
other minds those complements of thought of which we 
were conscious in ourselves, we should never be able 
to communicate to others what engaged our interest, 
and man would remain for man, if an intelligence at 
all, a mere isolated intelligence. 

In regard to the question, — What may these sen- lutonations 
sible symbols be, by which we are to compass such the only 
memorable effects, — it is needless to show that mien sensible 
and gesture, which, to a certain extent, afford a kind of thought 
of natural expression, are altogether inadequate to the numication. 
double purpose of thought and communication, which 
it is here required to accomplish. This double pur- 
pose can be effected only by symbols, which express, 
through intonations of the voice, what is passing in 
the mind. These vocal intonations are either inarti- These m- 
culate or articulate. The former are mere sounds or and*^rrtl-^ 
cries ; and, as such, an expression of the feelings of '''''''^' 
which the lower animals are also capable. The latter The latter 

. P constitute 

constitute words, and these, as the expression oi Language 
thoughts or notions, constitute Language Proper or 
Speech.'* Speech, as we have said, as the instru- How Lan- 

. . . . guage is a 

ment of elaboratmoj, fixing, and communicating our source of 

Error. 

thoughts, is a principal mean of knowledge, and even 
the indispensable condition on which depends the ex- 
ercise of our higher cognitive faculties. But, at the 
same time, in consequence of this very dependence of 
thought upon language, inasmuch as language is itself 

a Cf. Krug, Lofjik, § 1 45. Anm. — Ed. 
VOL. IL K 



UQ 



LECTURES ON LOGIC. 



LECT 
XXXI. 



The ambi- 
guity of 
words the 
principal 
source of 
error origi- 
nating in 
Language. 



Two cir- 
cumstances 
under this 
head, wliich 
mutually 
affect each 
other. 



not perfect, the understanding is not only restrained 
in its operations, and its higher development, conse- 
quently, checked, but many occasions are given of 
positive error. For, to say nothing of the impedi- 
ment presented to the free communication of thought 
by the multitude of tongues into which human lan- 
guage is divided, in consequence of which all speech 
beyond their mother-tongue is incomprehensible to 
those who do not make a study of other languages, — 
even the accurate learning of a single language is at- 
tended with such difficulties, that perhaps there never 
yet has been found an individual who was thoroughly 
acquainted with all the words and modes of verbal 
combination in any single language, — his mother- 
tongue even not excepted. But the circumstance of 
principal importance is, that, how copious and expres- 
sive soever it may be, no language is competent ade- 
quately to denote all possible notions, and all possible 
relations of notions, and from this necessary poverty 
of language in all its different degrees, a certain in- 
evitable ambiguity arises, both in the employment 
of single words and of words in mutual connection. 

As this is the principal source of the error originat- 
ing in Language, it will be proper to be a little more 
explicit. And here it is expedient to take into ac- 
count two circumstances, which mutually affect each 
other. The first is, that as the vocabulary of every 
language is necessarily finite, it is necessarily disj^ro- 
portioned to the multiplicity, not to say infinity, of 
thought ; and the second, that the complement of 
words in any given language has been always filled 
up with terms significant of objects and relations of 
the external world, before the want was experienced 



LECTUllES ON LOGIC. 147 

of words to express the obiects and relations of the lect. 

. ^ 1 ^ '' XXXI. 

internal. 



From the first of these circumstances, considered The voca- 
exclusively and by itself, it is manifest that one of every Lan- 

1 • T 1 TT 1 1 1 guageneces- 

two alternatives must take place. Jidther the words sariiy finite. 

f, I 11- 1 • 1 Consequen- 

01 a language must each designate only a single ces of this. 
notion, — a single fasciculus of thought, — the multitude 
of notions not designated being allowed to perish, 
never obtaining more than a momentary existence in 
the mind of the individual ; or the words of a language 
must each be employed to denote a plurality of con- 
cepts. In the former case, a small amount of thought 
would be expressed, but that precisely and without 
ambiguity ; in the latter, a large amount of thought 
would be expressed, but that vaguely and equivocally. 
Of these alternatives, (each of which has thus its ad- 
vantages and disadvantages), — the latter is the one 
which has universally been preferred ; and, accord- 
ingly, all languages by the same word express a mul- 
titude of thoughts, more or less differing from each 
other. Now what is the consequence of this "? It is 
plain that if a word has more than a single mean- 
ing attached to it, when it is employed it cannot of 
itself directly and peremptorily suggest any definite 
thought ; — all that it can do is vaguely and hypothe- 
ticaUy to suggest a variety of different notions ; and 
we are obliged from a consideration of the context, — 
of the tenor, — of the general analogy, of the discourse, 
to surmise, with greater or less assurance, with greater 
or less precision, what particular bundle of characters 
it was intended to convey. Words, in fact, as Ian- words are 
guages are constituted, do nothing more than sug- hints L 
gest, — are nothing more than hints ; hints, likewise, 



XXXI. 



148 LECTURES ON LOGIC. 

LECT. which leave the principal part of the process of inter- 
pretation to be performed by the mind of the hearer. 
In this respect, the effect of words resembles the effect 
of an outline or shade of a countenance with which 
we are familiar. In both cases, the mind is stimu- 
lated to fill up what is only hinted or pointed at. 
Thus it is that the function of laoguage is not so much 
to infuse knowledge from one intelligence to another, 
as to bring two minds into the same train of thinking, 
and to confine them to the same track. In this pro- 
cedure what is chiefly wonderful, is the rapidity with 
which the mind compares the word with its correla- 
tions, and, in general, without the slightest effort, de- 
cides which among its various meanings is the one 
which it is here intended to convey. But how mar- 
vellous soever be the ease and velocity of this process 
of selection, it cannot always be performed with equal 
certainty. Words are often employed with a plural- 
ity of meanings ; several of which may quadrate, or 
be supposed to quadrate, with the general tenor of the 
discourse. Error is thus possible ; and it is also pro- 
bable, if we have any prepossession in favour of one 
interpretation rather than of another. So copious a 
source of error is the ambiguity of language, that a 
very large proportion of human controversy has been 
concerning the sense in which certain terms should 
be understood ; and many disputes have even been 
fiercely waged, in consequence of the disputants being 
unaware that they agreed in opinion, and only differed 
in the meaning they attached to the Avords in which 
that opinion was expressed. On this subject I may 
refer you to the very amusing and very instructive 
treatise of Werenfelsius, entitled De Logomachiis 
Eruditorum. 



LECTUEES ON LOGIC. 149 

" In regard to a remedy for this description of error, lect. 

• • . XXXI 

— this lies exclusively in a thorough study of the '. 



language employed in the communication of ki^ow- ^^™^^y. 
ledge, and in an acquaintance with the rules of Criti- fr'i^m^Ean- 
cism and Interpretation. The study of languages, s^^s^- 
when rationally pursued, is not so unimportant as 
many fondly conceive ; for misconceptions most fre- 
quently arise solely from an ignorance of words ; and 
every language may, in a certain sort, be viewed as a 
commentary upon Logic, inasmuch as every language, 
in like manner, mirrors in itself the laws of thought. 

" In reference to the rules of Criticism and Interpre- 
tation, — these especially should be familiar to those 
who make a study of the writings of ancient authors, 
as these writings have descended to us often in a very 
mutilated state, and are composed in languages which 
are now dead. How many theological errors, for ex- 
ample, have only arisen because the divines were 
either ignorant of the principles of Criticism and Iler- 
meneutic, or did not properly apply them ! Doctrines 
originating in a corrupted lection, or in a figurative 
expression, have thus arisen and been keenly defended. 
Such errors are best combated by philological weapons ; 
for these pull them up along with their roots. 

"A thorough knowledge of languages in general 
accustoms the mind not to remain satisfied with the 
husk, but to penetrate in, even to the kernel. AVith 
this knowledge we shall not so easily imagine that we 
understand a system, when we only possess the lan- 
guage in which it is expressed ; we shaU not conceive 
that we truly reason, when we only employ certain 
empty words and formulae ; we shall not betray our- 
selves into unusual and obscure expressions, under 
which our meaning may be easily mistaken ; finall3% 



150 LECTURES ON LOGIC. 

LECT. we shall not dispute with others about words, when we 

XXXI . • 

— 1-^ are in fact at one with them in reo;ard to thino;s."a 



So much for the errors which originate in Language. 
IV. Source As to thc last sourcc of Error which I enumerated, 

of Error, — 

the Objects — the Objects themselves of our knowledge, — it is 

of our 

knowledge, hardly necessary to say anything. It is evident that 
some matters are obscure and abstruse, while others 
are clear and palpable ; and that, consequently, the 
probability of error is greater in some studies than it 
is in others. But as it is impossible to deliver any 
special rules for these cases, different from those which 
are given for the Acquisition of Knowledge in gen- 
eral, concerning which we are soon to speak, — this 
source of error may be, therefore, passed over in 
silence. 

We have now thus jBnished the consideration of the 
various Sources of Error, and — 

Par. cv. IF CV. The following rules may be given, as 

touching the results of the foregoing discussion, touching 

and Reme- thc Causcs aud Eemcdics of our False Judgments. 

dies of our ^ _, - ... . . 

FaiseJudg- 1 . iLudeavour as lar as possible to obtain a 

clear and thorough insight into the laws of the 
Understanding, and of the Mental Faculties in 
general. Study Logic and Psychology. 

2°. Assiduously exercise your mind in the ap- 
plication of these laws. Learn to think method- 
ically. 

3°. Concentrate your attention in the act of 
Thinking ; and principally employ the seasons 
when the Intellect is alert, the Passions slumber- 
ing, and no external causes of distraction at work. 

a Krug, Logik, § 157. Anm. — Ed. 



ments. 



LECTURES ON LOGIC. 151 

4°. Carefully eliminate all foreign interests lect. 

A.XA.1, 



from the objects of your inquiry, and allow your- 
selves to be actuated by tlie interest of Truth 
alone. 

5°. Contrast your various convictions, your 
past and present judgments, with each other ; 
and admit no conclusion as certain, until it has 
been once and again thoroughly examined, and 
its correctness ascertained. 

6°. Collate your own persuasions with tliose 
of others ; attentively listen to and weigh, with- 
out prepossession, the judgments formed by 
others of the opinions which you yourselves 
maintain." 

a Cf. Krug, Lorjilc, § 160. Bachmann, Loffik, § 416. — Ed. 



]52 



LECTURES ON LOGIC. 



LECTURE XXXII. 

MODIFIED METHODOLOGY. 

SECTION I. — OF THE ACQUISITION OF KNOWLEDGE. 

L EXPERIENCE. — A. PERSONAL: — OBSERVATION 
INDUCTION AND ANALOGY. 



LECT. 
XXXIL 

Means by 
which our 
knowledge 
obtains the 
character of 
Perfection, 
viz. the 
Acquisition 
and the 
Communi- 
cation of 
Knowledge. 



The acqui- 
sition of 
Knowledge. 



Human 
Knowledge 
of two 
kinds. 



In our last Lecture, having concluded the Second 
Department of Concrete Logic, — that which treats of 
the Causes of Error, — we now enter upon the Third 
part of Concrete or Modified Logic, — that which con- 
siders the Means by which our Knowledge obtains the 
character of Perfection. These means may, in gen- 
eral, be regarded as two, — the Acquisition and the 
Communication of knowledge, — and these two means 
we shall, accordingly, consider consecutively and apart. 

In regard to the Acquisition of Knowledge, — we 
must consider this by reference to the difterent kinds 
of knowledge of which the human intellect is capable. 
And this, viewed in its greatest universality, is of two 
species. 

Human knowledge, I say, viewed in its greatest 
universality, is of two kinds. For either it is one of 
which the objects are given as contingent phsenomena ; 
or one in which the objects are given as necessary 
facts or laws. In the former case, the cognitions are 



LECTURES ON LOGIC. 153 

called empirical, experiential, or of exp)erience ; in the lect. 
latter, pure, intuitive, ratio7ial, or of reason, also of — I — 1 



common sense. These two kinds of knowledge are, 
likewise, severally denominated cognitions a ^oosteinori 
and cognitions a priori. The distinction of these two 
species of cognitions consists properly in this, — that 
the former are solely derived from the Presentations 
of Sense, External and Internal : whereas the latter, 
though first manifested on the occasion of such Pre- 
sentations, are not, however, mere products of Sense ; 
on the contrary, they are laws, principles, forms, no- 
tions, or by whatever name they may be called, native 
and original to the mind, that is, founded in, or con- 
stituting the very nature of. Intelligence ; and, ac- 
cordingly, out of the mind itself they must be deve- 
loped, and not sought for and acquired as foreign and 
accidental acquisitions. As the Presentative Facul- 
ties inform us only of what exists and what happens, 
that is, only of facts and events, — such empirical 
knowledge constitutes no necessary and universal 
judgment ; all, in this case, is contingent and particu- 
lar, for even our generalised knowledge has only a 
relative and precarious universality. The cognitions, 
on the other hand, which are given as Laws of Mind, 
are, at once and in themselves, universal and neces- 
sary. We cannot but think them, if we think at all. 
The doctrine, therefore, of the Acquisition of Ilnow- Doctrine of 
ledge, must consist of tw^o parts,- — the first treating ofsidonoT" 
the acquisition of knowledge through the data of Ex- consists'^ o!^ 
perience, the second, of the acquisition of knowledge ^''^ ^"''^''" 
through the data of Intelligence." 

a See Esser, Logik, § 145 Ed. called acquired, inasmuch as it is ac- 

In regard to the acquisition of quired either, 1 °, By experience ; or, 
knowledge, — all knowledge may be 2°, On occasion of experience. 



15-t LECTURES ON LOGIC. 

LECT. In reo-ard to the first of these sources, viz. Experi- 

XXXII . . 

—1 — '- ence, — this is either our own experience or the expe- 
tri Je' of^x- ^i^iic® of others, and in either case it is for us a mean 
ExpeH^nce ^f kuowledgc. It is manifest that the knowledge we 
kinds! acquire through our personal experience, is far supe- 
rior in degree to that which we obtain through the 
experience of other men ; inasmuch as our knowledge 
of an object, in the former case, is far clearer and more 
distinct, far more complete and lively, than in the 
latter ; while at the same time the latter also affords 
us a far inferior conviction of the correctness and cer- 
tainty of the cognition than the former. On the 
other hand, foreign is far superior to our proper expe- 
rience in this, — that it is much more comprehensive, 
and that, without this, man would be deprived of those 
branches of knowledge which are to him of the most 
indispensable importance. Now, as the principal dis- 
tinction of experience is thus into our own experience 
and into the experience of others, we must consider it 
more closely in this twofold relation.^ First, then, of 
our Personal Experience, 
1. Personal Experience necessarily supposes, as its primary con- 
dition, certain presentations by the faculties of Ex- 
ternal or of Internal Perception, and is, therefore, of 
two kinds, according as it is conversant about the 
objects of the one of these faculties, or the objects of 
the other. But the presentation of a fact of the ex- 
ternal or of the internal world is not at once an expe- 
rience. To this there is required, a continued series 
of such presentations, a comparison of these to- 
gether, a mental separation of the different, a mental 
combination of the similar, and it, therefore, over and 
above the operation of the Presentative Faculties, re- 

a Esser, Lor/ik, § 146. — Ed. 



LECTURES ON LOGIC. 155 

quires the co-operation of the Retentive, the Repro- lect. 

• • . XXXII 

ductive, the Representative, and the Elaborative — ^ — 1 



Faculties. In regard to Experience, as the first means 
by which we acquire knowledge through the legiti- 
mate use and application of our Cognitive Faculties, 
I give you the following paragraph : — 

H CVI. The First Mean towards the Acquisi- Par. cvi. 
tion of Knowledge is Experience (ex]jerieiitia,^Alt^—^n' 
ilxTTeipia). Experience may be, rudely and gener- ^^^^^ ' 
ally, described as the apprehension of the phse- 
nomena of the outer world, presented by the 
Faculty of External Perception, and of the 
phsenomena of the inner world, presented by the 
Faculty of Self-consciousness : — these phaenomena 
being retained in Memory, ready for Reproduc- 
tion and Representation, being also arranged into 
order by the Understanding. 

This paragraph, you will remark, affords only aExpiica- 
preliminary view of the general conditions of Expe- 
rience. In the first place, it is evident, that without 
the Presentative, or, as they may with equal propriety 
be called, the Acquisitive, Faculties of Perception, 
External and Internal, no experience would be pos- 
sible. But these faculties, though affording the fun- 
damental condition of knowledge, do not of themselves 
make up experience. There is, moreover, required 
of the phsenomena or appearances the accumulation 
and retention, the reproduction and representation. 
Memory, Reminiscence, and Imagination must, there- 
fore, also co-operate. Finally, unless the phsenomena 
be compared together, and be arranged into classes, 
according to their similarities and differences, it is 



156 LECTURES ON LOGIC. 

LFXT. evident that no iuclefments, — no conclusions, can be 

XXXII . 

1 formed concerning tliem ; but without a judgment 

knowledge is impossible ; and as experience is a know- 
ledge, consequently experience is impossible. The 
Understanding or Elaborative Faculty must, there- 
fore, likewise co-operate. Manilius has well expressed 
the nature of experience in the following lines : — 

" Per varies usus artem experientia fecit, 
Exemplo monstrante viam," " 

And Afranius in the others : — 

" Usus me geuuit, mater peperit Meraoria ; 
Sophiam vocant me Graii, vos Sapientiam,";3 

Common " Our owu obscrvation, be it external or internal, is 

and Scien- , . . 

tificEspe- either with, or without, intention ; and it consists 



rieuce. 



either of a series of Presentations alone, or Abstrac- 
tion and Keflection supervene, so that the presenta- 
tions obtain that completion and system which they 
do not of themselves possess. In the former case, the 
experience may be called an Unlearned or a Common; 
in the latter, a Learned ox Scientific Experience. In- 
tentional and reflective experience is called Ohser- 
observa- vatiou. Observation is of two kinds ; for either the 
what. objects which it considers remain unchanged, or, pre- 
kinds,— vious to its application, they are made to undergo 

Observation . , . , i i • 

Proper, and ccrtaiu arbitrary changes, or are placed in certain 
nient. factitious rclatious. In the latter case, the observation 
obtains the specific name of Eocperiment. Observation 
and Experiment do not, therefore, constitute opposite 
or two different procedures, — the latter is, in propriety, 
only a certain subordinate modification of the former; 
for, while observation may accomplish its end without 

o I. 61. f^is Poetarnm Lat'moruni, vol. ii. p. 

/3 Frarjmcntmn e Sella. Vide Cor- ISl.'?, Lond. 1713.— Ed. 



LECTURES ON LOGIC. 157 



experiment, experiment without observation is impos- lect. 
sible. Observation and experiment are manifestly __U__ 



exclusively competent upon the objects of our empiri- 
cal knowledge ; and they co-operate, equally and in 
like manner, to the progress of that knowledge, partly 
by establishing, partly by correcting, partly by ampli- 
fying it. Under observation, therefore, is not to be 
understood a common or unlearned experience, which 
obtrudes itself upon every one endowed with the ordi- 
nary faculties of Sense and Understanding, but an 
intentional and continued application of the faculties 
of Perception, combined with an abstractive and re- 
flective attention to an object or class of objects, a 
more accurate knowledge of which, it is proposed, by 
the observation, to accomplish. But in order that the Pr»cognita 
observation should accomplish this end, — more espe- tion. *^"'^ 
cially when the objects are numerous, and a systematic 
complement of cognitions is the end proposed, — it is 
necessary that we should know certain prsecognita, — 
1°. What we ought to observe ; 2°. How we ought 
to observe ; and 3°. By what means are the data of 
observation to be reduced to system. The fii'st of 
these concerns the Object; the second, the Procedure; 
the third, the scientific Completion, of the observa- 
tions. It is proper to make some general observa- 
tions in regard to these, in their order ; and first, 
of the Object of observation, — the ivliat we ought to 
observe. 

" The Object of Observation can only be some given First,— The 
and determinate phsenomenon, and this phsenomenon obiefva- 
either an external or an internal. Through obser- 
vation, whether external or internal, there are four This four- 
several cognitions which we propose to compass, — viz., 
to ascertain — 1°. What the Phoenomena themselves 



158 LECTURES ON LOGIC. 

LECT. are ; 2°. What are tlie Conditions of tlieir Reality ; 

L 3°. Wliat are the Causes of their Existence ; 4°. What 

is the Order of their Consecution. 
1°. What " In regard to what the phsenomena themselves 
nomenaare. are {quid siiit), that is, in regard to what constitutes 
their peculiar nature, — this, it is evident, must be the 
primary matter of consideration, it being always sup- 
posed that the fact (the an sit) of the phsenomenon 
itself has been established.'* To this there is required, 
In their abovc all, a clear and distinct Presentation or Repre- 
pVuTiarHies scutatiou of thc objcct. lu ordcr to obtain this, it 
trastsr' behoves us to analyse, — to dismember, the constituent 
parts of the object, and to take into proximate ac- 
count those characters which constitute the object, 
that is, which make it to be what it is, and nothing 
but what it is. This being performed, we must pro- 
ceed to compare it with other objects, and with those 
especially which bear to it the strongest similarity, 
taking accurate note always of those points in which 
they reciprocally resemble, and in which they recipro- 
cally disagree. 
As under " But it is not euougli to consider the several phse- 
geS anT Homcna in their individual peculiarities and contrasts, 
species. — ^^ what they are and in what they are not, — it is 
also requisite to bring them under determinate genera 
and species. To this end we must, having obtained 
(as previously prescribed) a clear and distinct know- 
ledge of the several phaenomena in their essential 
similarities and differences, look away or abstract 
from the latter, — the differences, and comprehend the 
former, — the similarities, in a compendious and char- 
acteristic notion, under an appropriate name. 

a Better the Aristotelic questions, p/iys/cs, vol. i. p. 56. — Ed.] 
- A n Sit, &c. [See Lectures on Mcta- 



LECTURES ON LOGIC. 159 

" When the distinctive peculiarities of the phse- lect. 

XXXII 

nomena have been thus defiuitively recognised, the 1 



second question emerges, — What are the Conditions ^^"^ what^ 
of their Reality. These conditions are commonly {[°°^.°f^^*^''^ 
called Requisites, and under requisite we must un- 
derstand all that must have preceded, before the 
phaenomena could follow. In order to discover the 
requisites, we take a number of analogous cases, or 
cases similar in kind, and inquire what are the cir- 
cumstances under which the phsenomenon always 
arises, if it does arise, and what are the circumstances 
under which it never arises ; and then, after a com- 
petent observation of individual cases, we construct 
the general judgment, that the phsenomenon never 
occurs unless this or that other phsenomenon has pre- 
ceded, or at least accompanied, it. Here, however, it 
must be noticed, that nothing can be viewed as a requi- 3°. AVhat 
site wdiich admits of any, even the smallest, exception. orthe'^Pha- 

" The requisite conditions being discovered, the ^^^^^^' 
third question arises, — What are the Causes of the 
Phsenomena. According to the current doctrine, the 
causes of phoenomena are not to be confounded with 
their requisites ; for although a phsenomenon no more 
occurs without its requisite than without its cause, 
still, the requisite being given, the phsenomenon does 
not necessarily follow, and, indeed, very frequently 
does not ensue. On the contrary, if the cause occurs, 
the phsenomenon must occur also. In other words, 
the requisite or condition is that without which the 
phsenomenon never is ; the cause, on the other hand, 
is that through which it always is. Thus an emotion 
of pity never arises without a knowledge of the mis- 
fortune of another ; but so little does this knowledge 
necessitate that emotion, that its opposite, a feeling 



1()0 LECTURES OX LOGIC. 

LECT. of rejoicii]g, complacency, at sucli suffering may ensue; 
'- whereas the knowledo-e of another's misfortune must 



be followed by a sentiment of pity, if we are predis- 
posed in favour of the person to whom the misfortune 
has occurred. In this view, the knowledge of another's 
misfortune is only a requisite ; whereas our favour- 
able predisposition constitutes the cause. It must, 
however, be admitted, that in different relations one 
and the same circumstance may be both requisite and 
cause ;"" and, in point of fact, it would be more cor- 
rect to consider the cause as the whole sum of ante- 
cedents, without which the ph?enomenon never does 
take place, and with which it always must. What 
are commonly called requisites, are thus, in truth, only 
partial causes ; what are called causes, only proximate 
requisites. 
4°. What " In the fourth place, having ascertained the essen- 
their Con- tial qualitics — the Conditions and the Causes of phe- 
nomena — a final question emerges, — AVhat is the Order 
in which they are manifested 'I and this being ascer- 
tained, the observation has accomplished its end. This 
question applies either to a phsenomenon considered 
in itself, or to a phsenomenon considered in relation 
to others. In relation to itself the question concerns 
only the time of its origin, of its continuance, and of 
its termination ; in relation to others, it concerns the 
reciprocal consecution in which the several phseno- 
mena appear."^ 
SecoiKi,— " We now go on to the Second Prsecognitum, — the 
of obser'"a-' Mauucr of Obscrvatiou, — How we are to observe. 
What we have hitherto spoken of, — the Object, — can 
be known only in one way, — the way of Scientific 
Observation. It, therefore, remains to be asked, — 

a Esser, Lor/!/.: § 148.— Ed. i8 //;/(/. 



LECTURES ON LOGIC. 161 

How must the observation be instituted, so as to lect. 
afford us a satisfactory result in regard to all the four —^ — - 
sides on which it behoves an object to be observed 1 state oUhe 
In the first place, as preliminary to observation, it iSmiuT"" 
required that the observing mind be tranquil and 
composed, be exempt from prejudice, partiality, and 
prepossession, and be actuated by no other interest 
than the discovery of truth. Tranquillity and com- 
posure of mind are of peculiar importance in our ob- 
servation of the phsenomena of the internal world ; 
for these phsenomena are not, like those of the exter- 
nal, perceptible by sense, enclosed in space, continu- 
ous and divisible ; and they follow each other in such 
numbers, and with such a rapidity, that they are at 
best observable with difficulty, often losing even their 
existence by the interference of the observing, — the re- 
flective energy, itself. But that the observation should 
be always conducted in the calm and collected state 
of mind required to purify this condition, we must 
be careful to obtain, more and more, a mastery over 
the Attention, so as to turn it with full force upon a 
single aspect of the phronomena, and, consequently, 
to abstract it altogether from every other. Its proper 
function is to contemplate the objects of observation 
tranquilly, continuously, and without anxiety for the 
result ; and this, likewise, without too intense an 
activity or too vigorous an application of its forces. 
But the observation and concomitant energy of atten- 2°. Condi- 
tion will be without result, unless we previously well questLi to 
consider what precise object or objects we are now to mineVby 
observe. Nor will our ex^^erience obtain an answer to ation. *^'^^' 
the question proposed for it to solve, unless that ques- 
tion be of such a nature as will animate the observing 
faculties by some stimulus, and give them a determi- 

VOL. IL L 



1G2 LECTURES ON LOGIC. 

LECT. nate direction. Wliere this is not the case, attention 

1 1 does not effect anything, nay, it does not operate at 

all. On this account such psychological questions as 
the following : What takes place in the process of 
Self- consciousness, — of Perception, — of Vision, — of 
Hearing, — of Imagination, &c., — cannot be answered, 
as thus absolutely stated, that is, without reference to 
some determinate object. But if I propose the pro- 
blem, — What takes place when I see this or that 
object, or better still, when I see this table, — the atten- 
tion is stimulated and directed, and even a child can 
give responses, which, if properly illustrated and ex- 
plained, will afford a solution to the problem. If, 
therefore, the question upon the object of observation 
be too vague and general, so that the attention is not 
suitably excited and applied, — this question must be 
divided and subdivided into others more particular, 
and this process must be continued until we reach a 
question which affords the requisite conditions. We 
should, therefore, determine as closely as possible the 
object itself, and the phases in which we wish to ob- 
serve it, separate from it all foreign or adventitious 
parts, resolve every question into its constituent ele- 
ments, enunciate each of these as specially as possible, 
and never couch it in vague and general expressions. 
But here we must at the same time take care, that the 
object be not so torn and mangled, that the attention 
feels no longer any attraction to the several parts, or 
that the several parts can no longer be viewed in their 
natural connection. So much it is possible to say in 
general, touching the Manner in which observation 
ought to be carried on ; what may further be added 
under this head, depends upon the particular nature 
of the objects to be observed."" 

a Esser, Lofjil; § 149.— Ed. 



LECTURES ON LOGIC. 168 

" In this manner, then, must we proceed, until all lect. 
has been accomplislied which the problem, to be an- 



swered by the observation, pointed out. When the 
observation is concluded, an accurate record or nota- 
tion of what has been observed is of use, in order to 
enable us to supply what is found wanting in our sub- 
sequent observation. If we have accumulated a con- 
siderable apparatus of results, in relation to the object 
we observe, it is proper to take a survey of these : 
from what is found defective, new questions must be 
evolved ; and an answer to these sought out through 
new observations. When the inquiry has attained 
its issue, a tabular view of all the observations made 
upon the subject is convenient, to afford a conspectus 
of the whole, and as an aid to the memory. But how. Third,— 
(and this is the Third Precognition), individual ob-bywhrch** 
servations are to be built up into a systematic whole, observatron 
is to be sought for partly from the nature of science in Suce^to 
general, partly from the nature of the particular em- ^J'^*^™- 
pirical science for the constitution of which the ob- 
servation is applied. Nor is what is thus sought 
difhcult to find. It is at once evident, that a syn- 
thetic arrangement is least applicable in the empirical 
sciences. For, anterior to observation, the object is 
absolutely unknown ; and it is only through observa- 
tion that it becomes a matter of science. We can, 
therefore, only go to work in a problematic or inter- 
rogative manner, and it is impossible to commence by 
assertory propositions, of which we afterwards lead 
the demonstration. We must, therefore, determine 
the object on aU sides, in so far as observation is com- 
petent to this ; we must analyse every question into 
its subordinate questions, and each of these must find 
its answer in observation. The systematic order is 
thus given naturally and of itself ; and in this pro- 



164 LECTURES ON LOGIC. 

LECT. cedure it is impossible that it sliould not be given. 
L But for a comprehensive and all-sided system of em- 
pirical knowledge, it is not sufficient to possess the 
whole data of observation, to have collected these to- 
gether, and to have arranged them according to some 
external principle ; it is, likewise, requisite that we 
have a thorough-going principle of explanation, even 
though this explanation be impossible in the way of 
observation, and a power of judging of the data, ac- 
cording to universal laws, although these universal 
laws may not be discovered by experience alone. 
These two ends are accomplished by different means. 
The former we compass by the aid of Hypothesis, the 
latter, by the aid of Induction and Analogy."" Of 
these in detail. In regard to Hypothesis, I give you 
the following paragraph. 

Par. cvii. H CVII. When a phaonomenon is presented, 

- what. ' which can be explained by no principle afforded 

through Experience, we feel discontented and un- 
easy; and there arises an effort to discover some 
cause which may, at least provisorily, account 
for the outstanding phasnomenon : and this cause 
is finally recognised as valid and true, if, through 
it, the given phccnomenon is found to obtain a 
full and perfect explanation. The judgment in 
which a phsenomenon is referred to such a pro- 
blematic cause, is called an Hi/j^othe^is/ 

Expiica- Hypotheses have thus no other end than to satisfy 



tion 



Hypothesis, the desire of the mind to reduce tlie oljjects of its 

— its end. 

a 'Eascr, Loffik, % ] 50. — Ed. hires on Metaphysics, vol. i. p. 168 

)8 Esser, Lurj'd; § 151. Cf. Lee- et seq. — Ed. 



LECTURES ON LOGIC. 165 

knowledge to unity and system ; and tliey do this in lect. 
recalling them, ad interim, to some principle, through — ^ — '- 



which the mind is enabled to comprehend them. From 
this view of their nature, it is manifest how far they 
are j^ermissible, and how far they are even useful and 
expedient ; throwing altogether out of account the 
possibility, that what is at first assumed as hypothet- 
ical, may, subsequently, be proved true. 

When our experience has revealed to us a certain 
correspondence among a number of objects, we are 
determined, by an original principle of our nature, to 
suppose the existence of a more extensive correspond- 
ence than our observation has already proved, or may 
ever be able to establish. This tendency to generalise 
our knowledge by the judgment, — that where much 
has been found accordant, all will be found accordant, 
— is not properly a conclusion deduced from premises, 
but an original principle of our nature, which we may 
call that of Logical, or perhaps better, that of Philo- 
sophical, Pi'esumj^tion. This Presumption is of two 
kinds ; it is either Induction or Analogy, which, though 
usually confounded, are, however, to be carefully dis- 
tinguished. I shall commence the consideration of 
these by the following paragraph. 

IF CVIII. If we have uniformly observed, that Par. cyin. 
a number of objects of the same class (genus or and Ana- 
species) possess in common a certain attribute, 
we are disposed to conclude that this attribute is 
possessed by all the objects of that class. This 
conclusion is properly called an htference of 
Induction. Again, if we have observed that two 
or more things asjree in several internal and 



166 LECTURES ON LOGIC. 

LECT. essential characters, we are disposed to conclude 

L that they agree, likewise, in all other essential 

characters, that is, that they are constituents of 
the same class (genus or species). This conclu- 
sion is properly called an Inference of Analogy. 
The principle by which, in either case, we are 
disposed to extend our inferences beyond the 
limits of our experience, is a natural or ultimate 
principle of intelligence ; and may be called the 
principle of Logical, or, more properly, of Philo- 
sophical, Presumption.^ 

Expiica- " The reasoning by Induction and the reasoning by 
Induction Analogy have this in common, that they both conclude 
fJy,J?their from something observed to something not observed ; 
ami^dT&r- from somcthiug within to something beyond the sphere 
^^'^^' of actual experience. They differ, however, in this, 
that, in Induction, that which is observed and from 
which the inference is drawn to that which is not ob- 
served, is a unity in plurality : whereas, in Analogy, 
it is a plurality in unity. In other words, in Induc- 
tion, we look to the one in the many ; in Analogy we 
look to the many in the one : and while in both we 
conclude to the unity in totality, we do this, in Induc- 
tion, from the recognised unity in plurality, in Analogy, 
from the recognised plurality in unity. Thus, as induc- 
tion rests upon the principle, that what belongs, (or does 
not belong), to many things of the same kind, belongs, 
(or does not belong), to all things of the same kind ; 
so analogy rests upon the principle, — that things which 
have many observed attributes in common, have other 



a Cf. Esser, Lorjih, §§ 140, 152. Systema Lorjicum, §§ 572, 573. Nuii- 
Kriig, Lorjik, §§ 166, 167, 168. — Ed. nesius, Dc Constitullone Artis Dia- 
[W o\i, Phil. Rat ionalis, § 479. Reusch, Iccticw, p. 126.] 



LECTURES ON LOGIC. 167 

not observed attributes in common likewise."" It is lect. 

XXXII 

hardly necessary to remark that we are now speaking 

of Induction and Analogy, not as principles of Pure 
Logic, and as necessitated by the fundamental laws 
of thought, but of these as means of acquiring know- 
ledge, and as legitimated by the conditions of objective 
reality. In Pure Logic, Analogy has no place, and 
only that induction is admitted, in which all the 
several parts are supposed to legitimate the inference 
to the whole. Aj^j^lied Induction, on the contrary, 
rests on the constancy, — the uniformity, of nature, 
and on the instinctive expectation we have of this 
stability. This constitutes what has been called the 
principle of Logical Presumption, though perhaps it 
might, with greater propriety, be called the principle 
of Philosophical Presumption. We shall now con- 
sider these severally ; and, first, of Induction. 

An Induction is the enumeration of the parts, in induction, 
order to legitimate a judgment in regard to the 
whole." Now, the parts may either be individuals or 
particulars strictly so called. I say strictly so called, 
for you are aware that the term particular is very 
commonly employed, not only to denote the species, as 
contained under a genus, but, likewise, to denote the 
individual, as contained under a species. Using, how- 
ever, the two terms in their proper significations, I 
say, if the parts are individual or singular things, the 
induction is then cdXl^di I aclividual ; whereas if the o; two 
parts be species or subaltern genera, the induction individual 
then obtains the name of Special. An example of '"' ^"""^ 
the Individual Induction is given, were we to argue 

a Esser, Lorjik, § 152.— Ed. Arabum, p. 36.) Bonnaj, 1836. Zaba- 

j8 [Cf. Ah u, All (Avicenncv) Viri ve\\A,Opera Logica,DeNatura Lo(jic(X, 

Docti, Be Logica Poema, 1. 190. (In L. i. c. 18, p. 45.] 

Schmolders, Bocumenta PMlosopMce 



168 LECTURES ON LOGIC. 

LECT. tlius, — Mercury, Venus, the Earth, Mars, c&c., are 

L bodies in themselves opaque, and ivhich horroiv their 

light from the sun. But Mercury, Venus, &c., are 
planets. Tlierefore, all planets are opaque, and hor- 
roiv their liglvt from the sun. An example of the 
special is given, were we argue as follows, — Quadru- 
peds, birds, fishes, the amphibia, &c., all have a 
nervous system. But quadrupeds, birds, &c., are 
animals. Therefore all animals, (tlioiigli it is not yet 
detected in some), have a nervous system. Now, liere 
it is manifest that Special rests upon Individual in- 
duction, and that, in the last result, all induction is 
individual. For we can assert nothing concerning 
species, unless what we assert of them has been pre- 
viously observed in their constituent singulars.a 
Twocou- For a legitimate Induction there are requisite at 
legitrmate Icast two couditions. In the first place, it is necessary, 
That the partial (and this word I use as including both 
the terms individual and particular), — I say, it is ne- 
cessary that the partial judgments out of which the 
total or general judgment is inferred, be all of the 
same quality. For if one even of the partial judg- 
ments had an opposite quality, the whole induction 
would be subverted. Hence it is that we refute uni- 
versal judgments founded on an imperfect induction, 
by bringing what is called an instance (instantia), 
that is, by adducing a thing belonging to the same 
class or notion, in reference to which the opposite 
holds true. For example, the general assertion. All 
dogs bark, is refuted by the instance of the dogs of 
Labrador or California (I forget which), — these do not 
bark. In like manner, the general assertion. No qua- 
druped is oviparous, is refuted by the instance of the 

a Krug, Loijil; § 1G7. Anm.— Ed. /3 Esser, Lorjik, § 15-2.— Ed. 



luduC' 

tion,— 

First. 



LECTURES ON LOGIC. 109 

Ornithorhynchus Paradoxus. But tliat the universal ^^^^ 

jiiclgment must liave the same quahty as the partial, 

is self-evident ; for this judgment is simply the asser- 
tion of something to be true of all which is true of 
many. 

The second condition required is, That a competent Second. 
]mmber of the partial objects from which the induc- 
tion departs should have been observed, for otherwise 
the comprehension of other objects under the total 
judgment would be rash." What is the number of 
such objects, which amounts to a competent induc- 
tion, it is not possible to say in general. In some 
cases, the observation of a very few particular or indi- 
vidual examples is sufficient to warrant an assertion in 
regard to the whole class ; in others, the total judgment 
is hardly competent, until our observation has gone 
through each of its constituent parts. This distinc- 
tion is founded on the difference of essential and un- 
essential characters. If the character be essential to 
the several objects, a comparatively limited observa- 
tion is necessary to legitimate our general conclusion. 
For example, it would require a far less induction to 
prove that all animals breathe, than to prove that the 
mammalia, and the mammalia alone, have lateral 
lobes to the cerebellum. For the one is seen to be a 
function necessary to animal life ; the other, as far as 
our present knowledge reaches, appears only as an 
arbitrary concomitant. The difference of essential 
and accidental is, however, one itself founded on in- 
duction, and varies according to the greater or less 
perfection to which this has been carried. In the pro- 
gress of science, the lateral lobes of the cerebellum 
may appear to future physiologists as necessary a 

a Es.ser, Lo(/il-, % 152. — Ed. 



170 LECTURES ON LOGIC. 

LECT. condition of the function of sucklino; their yonncy, as 

XXXTT . . . 

1 the organs of breathing appear to us of circulation 

and of life. 

Summary To suui up tlio Doctriue of luduction, — " This is 

doctrine of morc ccrtaiu, 1°, In proportion to the number and 
diversity of the objects observed ; — 2°, In proportion 
to the accuracy with which the observation and com- 
parison have been conducted ; — 3°, In proportion as 
the agreement of the objects is clear and precise ; — 
and, 4°, In proportion as it has been thoroughly ex- 
plored, whether there exist exceptions or not."« 

Almost all induction is, however, necessarily imper- 
fect ; and Logic can inculcate nothing more import- 
ant on the investigators of nature than that sobriety 
of mind, which regards all its past observations only 
as hypothetically true, only as relatively complete, 
and which, consequently, holds the mind open to 
every new observation, which may correct and limit its 
former judgments. 

Analogy,— So much for Inductiou ; now for Analogy. Ana- 
logy, in general, means proportion, or a similarity of 
relations. Thus, to judge analogically or according to 
analogy, is to judge things by the similarity of their 
relations. Thus when we judge that as two is to 
four, so is eight to sixteen, we judge that they are 
analogically identical ; that is, though the sums in 
other respects are different, they agree in this, that 
as two is the half of four, so eight is the half of 
sixteen. 

In common language, however, this propriety of 
the term is not preserved. For by analogy is not 
always meant merely by proportiofi but frequently 
by comparison — by relation, or simply by similarity. 

a Esser, Logih, § 152.— Ed. 



what 



LECTURES ON LOGIC. l7l 

In so far as Analoo;y constitutes a particular kind of lect. 

XXXII 

reasoning from the individual or particular to the '- 



universal, it signifies an inference from the partial 
similarity of two or more things to their complete or 
total similarity. For example, — This disease corre- 
sponds in many symptoms ivith iJiose we have observed 
in typhus fevers ; it ivill, therefore, correspond in all, 
that is, it is a typhus fever. '^ 

Like Induction, Analogy has two essential requi- Has two 
sites. In the first place, it is necessary that of two condi-"" 
or more things a certain number of attributes should F^°st. 
have been observed, in order to ground the inference 
that they also agree in those other attributes, Tvhich 
it has not yet been ascertained that they possess. It 
is evident that in proportion to the number of points 
observed, in which the things compared together coin- 
cide, in the same proportion can it be with safety as- 
sumed, that there exists a common principle in these 
things, on which depends the similarity in the points 
known as in the points unknown. 

In the second place, it is required that the predi- second, 
cates already observed should neither be all negative 
nor all contingent ; but that some at least should be 
positive and necessary. Mere negative characters 
denote only what the thing is not ; and contingent 
characters need not be present in the thing at all. In 
regard to negative attributes, the inference, that two 
things, to which a number of qualities do not belong, 
and which are, consequently, similar to each other only 
in a negative point of view, — that these things are, 
therefore, absolutely and positively similar, is highly 
improbable. But that the judgment in reference to 

a Cf. Krug, Zor/yX', § 168. Anm. — '^c\\vao\(}iers, Documenta Phil. Arahum, 
Ed. [Condillac, L'Art dc Eaisonner, p. 36.) Whately, Rhetoric, p. 74.] 
I L. iv. ch. 3, p. 159. Avicenna, (in 



172 



LECTURES ON LOGIC. 



LECT. 
XXXII. 



Summary 
of the 
doctrine of 
Analogy, 



Induction 
and Ana- 
logy com- 
pared to- 
gether. 



the compared things (say A and X) must be of the 
same quality {i.e. either both affirmative or both nega- 
tive), is self-evident. For if it be said A is B, X is 
not B, A is not G, 'X. is C ; their harmony or simi- 
larity is subverted, and we should rather be war- 
ranted in arguing their discord and dissimilarity in 
other points. And here it is to be noticed that Ana- 
logy differs from Induction in this, that it is not 
limited to one quality, but that it admits of a mix- 
ture of both. 

In regard to contingent attributes, it is equally 
manifest that the analogy cannot proceed exclusively 
upon them. For, if two things coincide in certain 
accidental attributes (for example, two men in respect 
of stature, age, and dress), the supposition that there 
is a common principle, and a general similarity 
founded thereon, is very unlikely. 

To conclude : Analogy is certain in proportion, 
1°, To the number of congruent observations ; 2°, To 
the number of congruent characters observed ; 3°, To 
the importance of these characters and their essenti- 
ality to the objects; and, 4°, To the certainty that the 
characters really belong to the objects, and that a 
partial correspondence exists.* Like Induction, Ana- 
logy can only pretend at best to a high degree of 
probability ; it may have a high degree of certainty, 
but it never reaches to necessity. 

Comparing these two processes together : — " The 
Analogical is distinguished from the Inductive in this 
— that Induction regards a single predicate in many 
subjects as the attribute Z in A, in B, in C, in D, 
in E, in F, &c. ; and as these many belong to one 
class, say Q ; it is inferred that Z will, likewise, be 



a Esser, Lofjlk, § 152. Cf. Krug, Loffik, § 168. Anm. — Ed. 



LECTURES ON LOGIC. 173 

met witli in the otlier things belongino; to this class, lect. 

XXXII 

that is, in all Qs. On the other hand. Analogy re- 111 — 1 
gards many attributes in one subject (say m, 7i, o, p, 
in A) ; and as these many are in part found in 
another subject (say m, and n, in B), it is concluded 
that, in that second thing, there will also be found the 
other attributes (say o and p). Through Induction 
we, therefore, endeavour to prove that one character 
belongs, (or does not belong), to all the things of a 
certain class, because it belongs, (or does not belong), to 
many things of that class. Through Analogy, on the 
otlier hand, we seek to prove that all the characters 
of a thing belong, (or do not belong), to another or 
several others, because many of these characters be- 
long to this other or these others. In the one it is 
proclaimed, — One in many, therefore one in all. — In 
the other it is proclaimed, — Many in one, therefore all 
in one!'^ 

" By these processes of Induction and Analogy, as luductiou 
observed, we are unable to attain absolute certainty ; iog>- do not 
—a great probability is all that we can reach, and lute eer- 
this for the simple reason, that it is impossible, 
under any condition, to infer the unobserved from 
the observed,— the whole from any proportion of the 
parts, — in the way of any rational necessity. Even 
from the requisites of Induction and Analogy, it is 
manifest that they bear the stamp of uncertainty ; 
inasmuch as they are unable to determine how many 
objects or how many characters must be observed, in 
order to draw the conclusion that the case is the same 
with all the other objects, or with all the other char- 
acters. It is possible only in one way to raise Induc- 
tion and Analogy from mere probability to complete 

o Krug, Lmjik, § 168. Anm. — Ed. 



XXXII 



174 LECTURES ON LOGIC. 

LECT. certainty, — viz. to demonstrate that the principles 
which lie at the root of these processes, and which 
we have already stated, are either necessary laws of 
thought, or necessary laws of nature. To demonstrate 
that they are necessary laws of thought is impossible ; 
for Logic not only does not allow inference from 
many to all, but expressly rejects it. Again, to de- 
monstrate that they are necessary laws of nature is 
equally impossible. This has indeed been attempted, 
from the uniformity of nature, but in vain. For it is 
incompetent to evince the necessity of the inference of 
Induction and Analogy from the fact denominated 
the laiv of nature ; seeing that this law itself can only 
be discovered by the way of Induction and Analogy. 
In this attempted demonstration there is thus the 
most glaring j^eiii^o ^97*Z7^cipiV. The result which has 
been previously given remains, therefore, intact : — 
Induction and Analogy guarantee no perfect cer- 
tainty, but only a high degree of probability, while all 
probability rests at best upon Induction and Analogy, 
and nothing else."" 

a Esser, LogiJc, §152. — Ed. [On et seq. lIoSha,\ier,A7ifaiigsffru7ideder 

history and doctrine of the Logic of Lor/ik, § 422 et seq. Bolzano, Loyih, 

Probabilities, see Leibnitz, Nov.veaux vol. ii. § 161, vol. iii, § 317. Bachmann, 

Essais, L. iv. ch. xv. p. 425, ed. Raspe. Logil:, § 229 et seq. Fries, Lo<jik, § 

Wolf, Phil. Rat. § 564 et seq. Platner, 96 et seq. Prevost, Essais de Philo- 

Phil. Aphorismen, § 701 (old edit.) § sophie, ii. L. i. part iii. p. 56. Kant, 

594 (new edit.) Zedler, Lexikon, v. Logik, Einleitung x. Jacob, Grun- 

Wahrschei7ilich.'Wa.lch.,Lexil-on,Jbid. driss der Allgemeinen Logik, § 358, 

Lambert, Neues Organon, ii. p. 318 p. 131 et seq., 1800, Halle. Metz, 

et seq. Reusch, Systema Logicmn, § Institutiones Logiae, § 230 et seq., p. 

653 et seq. Hollmann, Logica, § 215 171, 1796.] 



LECTURES ON LOGIC. 175 



LECTURE XXXIII. 

MODIFIED METHODOLOGY. 

SECTION I. — OF THE ACQUISITION OF KNOWLEDGE. 

I. EXPERIENCE. B. FOREIGN : ORAL TESTIMONY 

— ITS CREDIBILITY. 

Having, in our last Lecture, terminated the Doctrine lect. 

XXXIII 

of Empirical Knowledge, considered as obtained Im- 



erience. 



mediately — that is, through the exercise of our own Expemi 
powers of Observation, — we are now to enter on the 
doctrine of Empirical Knowledge, considered as ob- 
tained Mediately — that is, through the Experience of 
Other Men. The following paragraph will afford you 
a general notion of the nature and kinds of this 
knowledge : — 

II CIX. A matter of Observation or Empiri- Par.cix. 
cal Knowledge can only be obtained Mediately, 
that is, by one individual from another, through 
an enouncement declaring it to be true. This 
enouncement is called, in the most extensive sense 
of the word, a Witnessing or Testimony, {testimo- 
nium) ; and the person by whom it is made is, 
in the same sense, called a Witness, or Testijier, 
(testis). The object of the Testimony is called 



17G 



LECTURES ON LOGIC. 



LECT. 

xxxin. 



the Fact, {factum); and its validity constitutes 
what is styled Historical Credibility, {credihilitas 
historica). To estimate this credibility, it is re- 
quisite to consider — 1°, The Subjective Trust- 
worthiness of the Witnesses, (Jides testium), and 
2°, The Objective Probability of the Fact itself. 
The former is founded partly on the Sincerity, 
and partly on the Competence, of the Witness. 
The latter depends on the Absolute and Eelative 
Possibility of the Fact itself. Testimony is either 
Immediate or Mediate. Immediate, where the 
fact reported is the object of a Personal Expe- 
rience ; Mediate, where the fact reported is the 
object of a Foreign Experience." 



Explica- 
tioa. 



" It is manifest that Foreign Experience, or the ex- 
perience of other men, is astricted to the same laws, 
and its certainty measured by the same criteria, as the 
experience we carry through ourselves. But the expe- 
rience of the individual is limited, when compared 
with the experience of the species ; and if men did 
not possess the means of communicating to each 
other the results of their several observations, — were 
they unable to co-operate in accumulating a stock 
of knowledge, and in carrying on the progress of dis- 
covery, — they would never have risen above the very 
lowest steps in the acquisition of science. But to this 
mutual communication they are competent; and each 
individual is thus able to appropriate to his own 
benefit the experience of his fellow-men, and to confer 
on them in return the advantages which his own ob- 
servations may supply. But it is evident that this reci- 



u Krug, Lxjll-, § 172— Ed. [Of. Scheibler, Topkn, c. 31.] 



LECTURES ON LOGIC. 177 

procal communication of their respective experiences lect. 
among men, can only be effected inasmuch as one is " 
able to inform another of what he has himself ob- 
served, and that the vehicle of this information can 
only be some enouncement in conventional signs of 
one character or another. The enouncement of what 
has been observed is, as stated in the paragraph, 
called a ivitnessing, — a hearing ivitness, — a testimo7iy, 
ko,., these terms being employed in their wider accep- 
tation ; and he by whom this declaration is made, 
and on whose veracity it rests, is called a ivitness, 
voucher, or testijier (testis)!'"' The term testimony, I 
may notice, is sometimes, by an abusive metonym, 
employed for untness ; and the word evidence is often 
ambiguously used for testimony, and for the bearer of 
testimony, — the ivitness. 

" Such an enouncement, — such a testimony, is, how- The proper 
ever, necessary for others, only when the experience Tistlmony. 
which it communicates is beyond the compass of their 
own observation. Hence it follows, that matters of 
reasoning are not proper objects of testimony, since 
matters of reasoning, as such, neither can rest nor 
ought to rest on the observations of others ; for a 
proof of their certainty is equally competent to all, 
and may by all be obtained in the manner in which it 
was originally obtained by those who may bear wit- 
ness to their truth. And hence it further follows, that 
matters of experience alone are proper objects of tes- 
timony ; and of matters of experience themselves, such 
only as are beyond the sphere of our personal expe- 
rience. Testimony, in the strictest sense of the term, 
therefore, is the communication of an experience, or, 

a Esser, Lofjil; § 1 53. — Ed. 
VOL. IL M 



178 



LECTURES ON LOGIC. 



LECT. 
XXXIII. 



Tlie Fact. 



Eye-wit- 
ness. 
Ear-wit- 
ness. 



what amounts to the same thing, the report of an 
observed phsenomenon, made to those whose own 
experience or observation has not reached so far. 

"The object of testimony, as stated in the para- 
graph, is called the fact ; the validity of a testimony 
Historical is Called historical credihility. The testimony is either 

credibility. . . . '^ . "^ . 

immediate or mediate. Immediate, when the witness 
has himself observed the fact to which he testifies ; 
mediate, when the witness has not himself had experi- 
ence of this fact, but has received it on the testimony 
of others. The former, the immediate witness, is 
commonly styled an eye-witness {testis oculatus) ; and 
the latter, the mediate witness, an ear-ivitness [testis 
auritus). The superiority of immediate to mediate 
testimony is expressed by Plautus, ' Pluris est oculatus 
testis unus, quam auriti decem.'" These denominations, 
eye and ear witness, are, however, as synoyms of im- 
mediate and mediate witness, not always either appli- 
cable or correct. The person on whose testimony a 
fact is mediately reported, is called the guarantee, or 
he on whose authority it rests ; and the guarantee 
himself may be again either an immediate or a medi- 
ate witness. In the latter case he is called a second- 
hand or intermediate ivitness ; and his testimony is 
commonly styled hearsay evidence. Further, Testi- 
mony, whether immediate or mediate, is either partial 
or complete ; either consistent or contradictory. These 
distinctions require no comment. Finally, testimony 
is either direct or indii^ect ; direct, when the witness 
has no motive but that of making known the fact ; 
indirect, when he is actuated to this by other ends."^ 



The Guar- 
antee. 



Tcstimouics 
— Partial, 
Complete, 
Consistent, 
Contradic- 
tory. 



a Truculentus, II. vi. 8. Cf. Kru^ 
Loijlk, § 172. Aum. — FiD. 



/3 Esser, Lorjllc, § 153.— Ed. 



LECTURES ON LOGIC. 179 

The only question in reference to Testimony is that lect. 

• . . . XXXTII 

which regards its Credibility ; and the question con- H^ — '- 
earning the credibility of the witness may be compre- Se 'subjicf : 
hended under that touching the Credibility of Testi- buity^o'f" 
mony. The order I shall follow in the subsequent i^nJeS. 
observations is this, — I shall, in the first place, con- Kiity'i^''' 
sider the Credibility of Testimony in general ; and, in i^''iJ™ar^ 
the second, consider the Credibility of Testimony in its Inl^^e™'' 
particular forms of Immediate and Mediate. iieSate^ 

First, then, in regard to the Credibility of Testi- 
mony in general ; — When we inquire whether a cer- 
tain testimony is, or is not, deserving of credit, there 
are two things to be considered : 1°, The Object of 
the Testimony, that is, the fact or facts for the truth 
of which the Testimony vouches ; and, 2°, The Subject 
of the Testimony, that is, the person or persons by 
whom the testimony is borne. The question, therefore, 
concerning the Credibility of Testimony, thus natu- 
rally subdivides itself into two. Of these questions, 
the first asks, — What are the conditions of the 
credibility of a testimony by reference to what is 
testified, that is, in relation to the Object of the testi- 
mony ? The second asks, — What are the conditions 
of the credibility of a testimony by reference to him 
who testifies, that is, in relation to the Subject of the 
testimony 1 " Of these in their order. 

On the first question. — " In regard to the matter i. credi- 
testified, that is, in regard to the object of the testi- Testimony 
mony; it is, first of all, a requisite condition, that i°, The 
what is reported to be true should be possible, both the"'Testi- 
absolutely, or as an object of the Elaborative Faculty, its Absolute 
and relatively, or as an object of the Presentative '^'" ' ' ^' 

a Cf. Esser, Logik, § 154. — Ed. 



180 LECTURES ON LOGIC. 

LECT. Faculties, — Perception, External or Internal. A tiling 
'- is possible absolutely, or in itself, when it can be con- 
strued to thought, that is, when it is not inconsistent 
with the logical laws of thinking ; a thing is relatively 
possible as an object of Perception, External or Inter- 
nal, w^hen it can affect Sense or Self-consciousness, 
and, through such affection, determine its apprehen- 
sion by one or other of these faculties. A testimony 
is, therefore, to be unconditionally rejected, if the fact 
which it reports be either in itself impossible, or im- 
possible as an object of the Presentative Faculties. 
Physical But the impossibility of a thing, as an obiect of these 

and Mcta- „ . ■•• "^ . .^ "^ . ^ 

physical faculties, must be decided either upon physical, or 

Impossi- . ,. 1 ' • T • ^^ 

biiity. upon metaphysical, principles. A thing is physically 
impossible as an object of sense, when the existence 
itself, or its perception by us, is, by the laws of the 
material world, impossible. It is metaphysically im- 
possible, when the object itself, or its perception, is pos- 
sible neither through a natural, nor through a super- 
natural, agency. But, to establish the physical impos- 
sibility of a thing, it is not sufficient that its existence 
cannot be explained by the ordinary laws of nature, 
or even that its existence should appear repugnant 
with these laws ; it is requisite that an universal and 
immutable law of nature should have been demon- 
strated to exist, and that this law would be subverted 
if the fact in question were admitted to be physically 
possible. In like manner, to constitute the metaphy- 
sical impossibility of a thing, it is by no means enough 
to show that it is not explicable on natural laws, or even 
that any natural law stands opposed to it ; it is further 
requisite to prove that the intervention even of super- 
natural agency is incompetent to its production, that 



LECTUEES ON LOGIC. 181 

its existence would involve the violation of some neces- lect. 

. . , „ XXXIII. 

sary principle oi reason. 



To establish the credibility of a testimony, in so Relative 

r ■... „. -,. Possibility 

lar as tins is regulated by the nature oi its object, of an object, 
there is, besides the proof of the absolute possibility 
of this object, required also a proof of its relative 
possibility ; that is, there must not only be no contra- 
diction between its necessary attributes, — the attri- 
butes by which it must be thought, — but no contra- 
diction between the attributes actually assigned to it 
by the testimony. A testimony, therefore, which, qua 
testimony, is self-contradictory, can lay no claim to 
credibility ; for what is self-contradictory is logically 
suicidal. And here the only question is, — Does the 
testimony, qua testimony, contradict itself "? for if the 
repugnancy arise from an opinion of the witness, apart 
from which the testimony as such would still stand 
undisproved, in that case the testimony is not at once 
to be repudiated as false. For example, it would be 
wrong to reject a testimony to the existence of a 
thing, because the witness had to his evidence of its 
observed reality annexed some conjecture in regard to 
its orioin or cause. For the latter mio-ht well be 
shown to be absurd, and yet the former would re- 
main unshaken. It is, therefore, always to be ob- 
served, — that it is only the self-contradiction of a 
testimony, qua testimony, that is, the self-contradic- 
tion of the fact itself, which is peremptorily and irre- 
vocably subversive of its credibility. 

" We now proceed to the second question ; that is, 2°, The 
to consider in general the Credibility of a Testimony tuV'Testi'- 
by reference to its Subject, that is, in relation to the jreisona7 
Personal Trustworthiness of the Witness. The trust- wcrthincss 



182 LECTURES ON LOGIC. 

LECT. worthiness of a witness consists of two elements or 
' conditions. In the first place, he must be willing, in 
wuness ^^^ sccoucl placc, hc must be able, to report the truth. 
Sts oTtwo "^^^ ^^'^^ ^^ these elements is the Honesty, — the Sin- 
a "^HTnest" verity, — thc Veracity ; the second is the Competency 
or Veracity, q£ ^j^g wltucss. Both are cqually necessary, and if 
one or other be deficient, the testimony becomes alto- 
gether null. These constituents, likewise, do not infer 
each other ; for it frequently happens that where the 
honesty is greatest the competency is least, and where 
the competency is greatest the honesty is least. But 
when the veracity of a witness is established, there is 
established also a presumption of his competency ; for 
an honest man will not bear evidence to a point in re- 
gard to which his recollection is not precise, or to the 
observation of which he had not accorded the re- 
quisite attention. In truth, when a fact depends 
on the testimony of a single witness, the competency 
of that witness is solely guaranteed by his honesty. 
In regard to the honesty of a witness, — this, though 
often admitting of the highest probability, never ad- 
mits of absolute certainty ; for, though, in many cases, 
we may know enough of the general character of the 
witness to rely with perfect confidence on his veracity, 
in no case can we look into the heart, and observe 
the influence which motives have actually had upon 
his volitions. We are, however, compelled, in many 
of the most important concerns of our existence, to 
depend on the testimony, and, consequently, to confide 
in the sincerity, of others. But from the moral con- 
stitution of human nature, we are warranted in pre- 
suming on the honesty of a witness ; and this pre- 
sumption is enhanced in proportion as the following 
circumstances concur in its confirmation. In the 



LECTURES ON LOGIC. ]83 

first place, a witness is to be presumed veracious in lect. 
this case, in proportion as his love of truth is already ^ ' ^ 
established from others. In the second place, a wit- Ju^p^tion of 
ness is to be presumed veracious, in proportion as he ora^vit-'^ 
has fewer and weaker motives to falsify his testimony, hanced by 
In the third place, a witness is to be presumed vera- IZl^ZnZl. 
cious, in proportion to the likelihood of contradiction 
which his testimony would encounter, if he deviated 
from the truth. So much for the Sincerity, Honesty, 
or Veracity of a witness. 

" In regard to the Competency or Ability of a wit- 1. compa. 
ness, — this, in general, depends on the supposition, that witness. 
he has had it in his power correctly to observe the 
fact to which he testifies, and correctly to report it. 
The presumption in favour of the competence of acircum- 
witness rises, in proportion as the following conditions which the 
are fulfilled : — In the fir&t place, lie must be presumed uonTcom- 
competent in reference to the case in hand, in propor- enhanced! 
tion as his general ability to observe and to commu- 
nicate his observation has been established in other 
cases. In the second place, the competency of a wit- 
ness must be presumed, in proportion as in the par- 
ticular case a lower and commoner amount of ability 
is requisite rightly to observe, and rightly to report 
the observation. In the third place, the competency 
of a witness is to be presumed, in proportion as it is 
not to be presumed that his observation was made or 
communicated at a time when he was unable correctly 
to make or correctly to communicate it. So much 
for the Competency of a witness. 

"Now, when both the 2;ood will and the ability, The credi- 

' "-" bility 01 

that is, when both the Veracity and Competence, ot a Testimony 
witness have been sufficiently established, the credi- dated he- 

. - . cause the 

bility of his testimony is not to be invalidated be-facttesti- 



184 



LECTURES ON LOGIC. 



LECT. 
XXXIII. 

fied is one 
out of the 
ordinary 
course of 
experience. 



Summary 
regarding 
the Credi- 
bility of 
Testimony 
in general. 



cause the fact wliicli it goes to prove is one out of tlie 
ordinary course of experience."' "^ Thus it woukl be 
false to assert, with Hume, that miracles, that is, sus- 
pensions of the ordinary laws of nature, are incap- 
able of proof, because contradicted by what we have 
been able to observe. " On the contrary, where the 
trustworthiness of a witness or witnesses is unim- 
peachable, the very circumstance that the object is 
one in itself unusual and marvellous, adds greater 
weight to the testimony ; for this very circumstance 
would itself induce men of veracity and intelligence 
to accord a more attentive scrutiny to the fact, and 
secure from them a more accurate report of their ob- 
servation. 

" The result of what has now been stated in regard 
to the credibility of Testimony in general, is : — That 
a testimony is entitled to credit, when the requisite 
conditions, both on the part of the object and on the 
part of the subject, have been fulfilled. On the part 
of the object these are fulfilled, when the object is 
absolutely possible, as an ol)ject of the higher faculty 
of experience, — the Understanding, — the Elaborative 
Faculty, and relatively possible, as an object of the 
low^er or subsidiary faculties of experience, — Sense, and 
Self-consciousness. In this case, the testimony, qua 
testimony, does not contradict itself. On the part of 
the subject, the requisite conditions are fulfilled, when 
the trustworthiness, that is, the veracity and compe- 
tency of the witness, is beyond reasonable doubt. In 
regard to the veracity of the witness, — this cannot be 
reasonably doubted, when there is no positive ground 
on which to discredit the sincerity of the witness, and 
when the only ground of doubt lies in the mere gen- 

a Esser, Lorjil-, § 154. — Ed. 



LECTURES ON LOGIC. 185 

eral possibility of deception. And in reference to tlie lect. 
. , . xxxin. 
competency of a witness, — this is exposed to no rea- -— - 

sonable objection, when the ability of the witness to 
observe and to communicate the fact in testimony can- 
not be disallowed. Having, therefore, concluded the 
consideration of testimony in general, we proceed to 
treat of it in special, that is, in so far as it is viewed 
either as Immediate or as Mediate." " Of these in their 
order. 

The special consideration of Testimony, w^hen that n. Testi- 
testimony is Immediate. — "An immediate testimony, special,, as 

... ,T IT- • i'iif> Immediate 

or testimony at nrst hand, is one m which the lact and Medi- 
reported is an object of the proper or personal expe- 1°, imme- 
rience of the reporter. Now it is manifest, that an mony. 
immediate witness is in general better entitled to cre- 
dit than a witness at second hand ; and his testimony 
rises in probability, in proportion as the requisites, 
already specified, both on the part of its object and on 
the part of its subject, are fulfilled. An immediate 
testimony is, therefore, entitled to credit, — 1°, In pro- 
portion to the greater ability with wdiich the observ- Conditions 
ation has been made ; 2°, In proportion to the less biiity. 
impediment in the way of the observation being per- 
fectly accomplished ; 3°, In proportion as w^hat was 
observed could be fully and accurately remembered ; 
and, 4°, In proportion as the facts observed and re- 
membered have been communicated by intelligible 
and unambifruous sio;ns. 

" Now% whether all these conditions of a higher whether 

clll tfiCSG 

credibility be fulfilled in the case of any immediate conditions 
testimony, — this cannot be directly and at once as- in the case 
certained ; it can only be inferred, with greater or mediate 
less certainty, from the qualities of the witness ; and, cannotX' 

directly 
a Esser, Lorjik, § 154. — Ed. ascertained. 



186 LECTUFxES ON LOGIC. 

LECT. consequently, tlie validity of a testimony can only be 

'. accurately estimated from a critical knowledge of the 

personal character of the witness, as given in his in- 
tellectual and moral qualities, and in the circum- 
stances of his life, which have concurred to modify 
and determine these. The veracity of a witness either 
is, or is not, exempt from doubt ; and, in the latter case, 
it may not only lie open to doubt, but even be ex- 
posed to suspicion. If the sincerity of the witness be 
indubitable, a direct testimony is always preferable to 
an indirect ; for a direct testimony being made with 
the sole intent of establishing the certainty of the fact 
in question, the competency of the witness is less ex- 
posed to objection. If, on the contrary, the sincerity 
of the witness be not beyond a doubt, and, still more, 
if it be actually suspected, in that case an indirect 
testimony is of higher cogency than a direct ; for 
the indirect testimony being given with another view 
than merely to establish the fact in question, the in- 
tention of the witness to falsify the truth of the fact 
has not so strong a presumption in its fiivour. If both 
the sincerity and the competency of the witness are 
altogether indubitable, it is then of no importance 
whether the truth of the fact l)e vouched for by a 
single witness, or by a plurality of witnesses. On the 
other hand, if the sincerity and competency of the 
witness be at all doubtful, the credibility of a testi- 
mony will be greater, the greater the number of the 
When testi- witucsscs by w^hom the fact is corroborated. But here 
tains the it is to bc cousidcred, that when there are a plurality 

highest „ . . •■ n 1 • • 

degree of 01 tcstimouies to tlic samc tact, these testimonies are 
either consistent or inconsistent. If the testimonies 
be consistent, and the sincerity and competency of all 
the witnesses complete, in that case the testimony 



probahitity. 



LECTURES ON LOGIC. 187 



attains the liighest degree of probability of wliicli any lect. 
testimony is capable. Again, if the witnesses be in- ^ ^ 



Negative 



Discre- 
pancy. 



consistent, — on this hypothesis two cases are pos- ^^^p, 
sible ; for either their discrepancy is negative, or it 
is positive. A negative discrepancy arises, w^here one 
witness passes over in silence what another witness 
positively avers. A positive discrepancy arises, where 
one witness explicitly affirms something, wdiich some- 
thing another witness explicitly denies. When the 
difference of testimonies is merely negative, we may 
suppose various causes of the silence ; and, therefore, 
the positive averment of one witness to a fact is not 
disproved by the mere circumstance, that the same 
fact is omitted by another. But if it be made out, 
that the witness who omits mention of the fact, could 
not have been ignorant of that fact had it taken place, 
and, at the same time, that he could not have passed 
it over without violating every probability of human 
action, — in this case, the silence of the one witness 
manifestly derogates from the credibility of the other 
witness, and in certain circumstances may annihilate 
it altogether. Where, again, the diflference is positive, 
the discrepancy is of greater importance, because, 
(though there are certainly exceptions to the rule), 
an overt contradiction is, in general and in itself, of 
stronger cogency than a mere non-confirmation by 
simple silence. Now the positive discrepancy of tes- 
timonies either admits of conciliation, or it does not. 
In the former case, the credibility of the several testi- 
monies stands intact ; and the discrepancy among the 
witnesses is to be accounted for by such circumstances 
as explain, without invalidating, the testimony con- 
sidered in itself. In the latter case, one testimony 
manifestly detracts from the credibility of another ; 



188 LECTURES ON LOGIC. 

LF.cT. for of incompatible testimonies, while botli cannot be 

XXXIII 

— ^ — '- true, the one must be false, when reciprocally contra- 
dictory, or they may both be false, when reciprocally 
contrary. In this case, the whole question resolves 
itself into one of the greater or less trustworthiness of 
the opposing witnesses. Is the trustworthiness of the 
counter-witnesses equally great ■? In that case, neither 
of the conflictive testimonies is to be admitted. Again, 
is the trustworthiness of the witnesses not upon a par'? 
In that case, the testimony of the witness whose trust- 
worthiness is the greater, obtains the preference, — and 
this more especially if the credibility of the other wit- 
nesses is suspected." "' 

So much for the Credibility of Testimon)^, considered 
in Sjiecial, in so far as that testimony is Immediate or 
at First Hand ; and I now, in the second place, pass on 
to consider, likewise in special, the Credibility of Testi- 
mony, in so far as that testimony is Mediate, or at 
Second Hand. 

2°, Mediate " A Mediate Testimony is one where the fact is an 

Testiraouv. ,. n t\ it c t^ • -r-\ 

object not oi rersonal, but oi loreign Jiixperience. 
Touching the credibility of a mediate testimony, this 
supposes that the report of the immediate, and that 
the report of the mediate, witness are both trust- 
worthy. Whether the report of the immediate w^itness 
be trustworthy, — this we are either of ourselves able to 
determine, viz., from our personal acquaintance with 
his veracity and competence ; or we are unable of 
ourselves to do this, in which case the credibility of 
the immediate must be taken upon the authority of 
the mediate witness. Here, however, it is necessary 
for us to be aware, that the mediate witness is pos- 

a Esser, Lor/ik, § 155. — Ed. 



LECTURES ON LOGIC. 189 

sessed of the ability requisite to estimate the credi- lect. 
bility of the immediate witness, and of the honesty to 1— ^ — '. 
communicate the truth without retrenchment or falsi- 
fication. Bnt if the trustworthiness both of the 
mediate and of the immediate witness be sufficiently 
established, it is of no consequence, in regard to the 
credibility of a testimony, whether it be at first hand 
or at second. Nay, the testimony of a mediate may 
even tend to confirm the testimony of an immediate 
witness, when his own competence fairly to appreciate 
the report of the immediate witness is indubitable. 
If, however, the credibility of the immediate witness be 
unimpeachable, but not so the credibility of the medi- 
ate, in that case the mediate testimony, in respect of its 
authority, is inferior to the immediate, and this in the 
same proportion as the credibility of the second hand 
witness is inferior to that of the witness at first hand. 
Further, mediate witnesses are either Proximate or Mediate 
Eemote ; and, in both cases, either Independent or De- are either 
pendent. The trustworthiness of proximate witnesses or™Remote, 
is, in general, greater than the trustworthiness of re- indepen- 
mote ; and the credibility of independent witnesses Dependent, 
greater than the credibility of dependent. The re- 
mote witness is unworthy of belief, when the inter- 
mediate links are w^anting between him and the 
original witness ; and the dependent witness deserves 
no credit, when that on which his evidence depends 
is recognised as false or unestablished. Mediate tes- 
timonies are, likewise, either direct or indirect ; and, 
likewise, when more than one, either reciprocally con- 
gruent or conflictive. In both cases the credibility of 
the witnesses is to be determined in the same manner 
as if the testimonies were immediate. 



lijO LECTUEES ON LOGIC. 

LECT. " The testimony of a plurality of mediate witnesses, 

XXXIII •/ 1- 'j^ 

'- where there is no recognised immediate witness, is 

Shat"''" called a rumour, if the witnesses be contemporaneous; 
Traditiou. ^^^ ,^ iraditiou, if the witnesses be chronologically suc- 
cessive. These are both less entitled to credit, in pro- 
portion as in either case a fiction or falsification of the 
fact is comparatively easy, and, consequently, com- 
paratively probable." '* 

a Easer, Loyilc, § 156. — Ed, 



LECTURES ON LOGIC. J 91 



LECTURE XXXIV. 

MODIFIED METHODOLOGY. 

SECTION I. — OF THE ACQUISITION OF KNOWLEDGE. 

I. EXPERIENCE. — B. FOREIGN : — RECORDED TESTIMONY 
AND WRITINGS IN GENERAL. 

II. SPECULATION. 

In our last Lecture, we were engaged in the considera- ^^iv 
tion of Testimony, and the Principles by which its Cre- 

,.,.,.. , -, .. , , Criticism of 

dibility IS governed, — on the supposition always that Recorded 

1 -Ti o ^ • 1 Testimony, 

we possess the veritable report oi the witness whose and of 

. . f. -^ . . Writings 

testimony it proiesses to be ; and on the supposition in general. 
that we are at no loss to understand its meaning and 
purport. But questions may arise in regard to these 
points, and, therefore, there is a further critical process 
requisite, in order to establish the Authenticity, — the 
Integrity, and the Signification, of the documents in 
which the testimony is conveyed. This leads us to the 
important subject, — the Criticism of Recorded Testi- 
mony, and of Writings in general. I shall comprise the 
heads of the following observations on this subject in 
the ensuing paragraph. 

H ex. The examination and judgment ofpar. ex. 
Writings professing to contain the testimony of andTuter- 
certain witnesses, and of Writings in General pro- p^*^*^^''""' 



192 LECTURES ON LOGIC. 

LECT. fessing to be the work of certain authors, is of 

1 two parts. For the inquiry regards either, 1°, 

The Authenticity of the document, that is, 
whether it be, in whole or in part, the product of 
its ostensible author ; for ancient writings in 
particular are frequently supposititious or inter- 
polated ; or 2°, It regards the Meaning of the 
words of which it is composed, for these, espe- 
cially when in languages now dead, are frequently 
obscure. The former of these problems is re- 
solved by the ^r^ of Criticism, (Critica), in the 
stricter sense of the term ; the latter by the Art 
of Interpretation, [Exegetica or Hermeneutica) . 
Criticism is of two kinds. If it be occupied with 
the criteria of the authenticity of a writing in its 
totality, or in its principal parts, it is called the 
Higher, and sometimes the Internal, Criticism. 
If, again, it consider only the integrity of particu- 
lar words and phrases, it is called the Lower, and 
sometimes the External, Criticism. The former 
of these may perhaps be best styled the Criticism 
of Authenticity ; — the latter, the Criticism of In- 
tegrity. 

The problem which Interpretation has to solve 
is, — To discover and expound the meaning of a 
writer, from the words in which his thou2;hts are 
expressed. It departs from the principle, that 
however manifold be the possible meanings of 
the expressions, the sense of the writer is one. 
Interpretation, by reference to its sources or sub- 
sidia, has been divided into the Grammatical, the 
Histo^ncal, and the Philosophical, Exegesis."' 

a Cf. Krug Loyik, § 177 fi scq. — Kiesewetter, Lvjll; ]i. ii. § 185 ct seq.] 
Ed. [Snell, Logik, p. ii. § 6 p. 195. 



LECTURES ON LOGIC. 193 

"Testimonies, especially when the ostensible wit- lect. 
nesses themselves can no longer be interrogated, may 



be snbjected to an examination under various forms ; ^^^^"'*' 
and this examination is in fact indispensable, seeing 
not only that a false testimony may be substituted for 
a true, and a testimony true upon the whole may yet be 
falsified in its parts, — a practice which prevailed to a 
great extent in ancient times ; while at the same time 
the meaning of the testimony, by reason either of the 
foreign character of the language in which it is ex- 
pressed, or of the foreign character of thought in which 
it is conceived, may be obscure and undetermined. 
The examination of a testimony is twofold, inasmuch The exa- 

. , . . n ' K ^ • • 1 niination of 

as it IS either an examination oi its Authenticity and a testimony 

T • • • o • HIT • rm • '■wofold, — 

Integrity, or an examination oi its Meaning. ihisofitsAu- 

PTT f, ... Til • thenticity 

twoiold process oi examination is applicable to testi- and integ- 
monies of every kind, but it becomes indispensable itsMeaning. 
when the testimony has been recorded in writing, and 
when this, from its antiquity, has come down to us 
only in transcripts, indefinitely removed from the ori- 
ginal, and when the witnesses are men differing 
greatly from ourselves in language, manners, customs 
and associations of thought. The solution of the Criticism, 
problem, — By what laws are the authenticity or 
spuriousness, the integrity or corruption, of a writing 
to be determined, — constitutes the Art of Criticism, in 
its stricter signification {Critica) ; and the solution of interpreta- 
the problem, — By what law is the sense or meaning 
of writing to be determined, — constitutes the Art of In- 
terpretation or Exposition {Hermeneutica, Exegetica). 
In theory. Criticism ought to precede Interpretation, 
for the question, — Who has spoken, naturally arises 
before the question, — How what has been spoken is to 
be understood. But in practice, criticism and inter- 

VOL. IL N 



194) LECTURES ON LOGIC. 

LECT. pretation cannot be separated ; for in application they 

'- proceed hand in hand." " 

I. Criticism. "First, then, of Criticism, and the question that pre- 
sents itself in the threshold is, — What are its Defini- 
tion and Divisions ? Under Criticism is to be under- 
stood the complement of logical rules, by which the 
authenticity or spuriousness, the integrity or interpo- 
lation, of a writing is to be judged. The problems 

itsprob- which it proposes to answer are — 1°, Does a writing 
really proceed from the author to whom it is ascribed ; 
and, 2°, Is a writing, as we possess it, in all its parts 
the same as it came from the hands of its author. 
The system of fundamental rules, which are supposed 
in judging of the authenticity and integrity of every 
writing, constitutes what is called the Doctinne of 

Universal U7iiversal Criticism ; and the system of particular 
rules, by which the authenticity and integrity of 
writings of a certain kind are judged, constitutes the 

Special doctrine of what is called Special Criticism. It is 
manifest, from the nature of Logic, that the doctrine i 

Universal of Uuivcrsal Criticism is alone within its sphere. Now 

aionrwi'thin Uuivcrsal Criticism is conversant either with the 

of L^gi^^ authenticity or spuriousness of a writing considered 
as a whole, or with the integrity or interpolation of 

Its Divi- certain parts. In the former case it is called Higher, ! 
in the latter Lower, Criticism ; but these denomina- 
tions are inappropriate. The one criticism has also 
been styled the Internal, the other the External ; but 
these appellations are, likewise, exceptionable ; and, 
perhaps, it would be preferable to call the former the ; 
Criticism of the Anthe7\ticity, the latter, the Criticism i 
of the Integrity, of a work. I shall consider these in 
particular, and, first, of the Criticism of Authenticity. 

a Esser, Logik, § 157 Ed. 



sions 



LECTURES ON LOGIC. 195 

"A proof of the authenticity of a writino;, more lect. 

XXXIV 

especially of an ancient writing, can be rested only 



upon two grounds, — an Internal and an External, — ofAuthen^ 
and on these either apart or in combination. By in- *'"*^' 
ternal grounds, we mean those indications of authen- 
ticity which the writing itself affords. By external 
grounds, we denote the testimony borne by other 
works of a corresponding antiquity, to the authen- 
ticity of the writing in question. 

" In reo;ard to the Internal Grounds ; — it is evident, a. internal 

^ _ _ Grounds. 

without enterins; upon details, that these cannot of These of 

^, themselves 

themselves, that is, apart from the external grounds, not sutE- 
afford evidence capable of establishino; beyond a doubt establish 

, -, . . f. . . ? „ the authen- 

the authenticity oi an ancient writing ; lor we can ticity of a 
easily conceive that an able and learned forger may 
accommodate his fabrications both to all the general 
circumstances of time, place, people, and language, 
under which it is supposed to have been written, and 
even to all the particular circumstances of the style, 
habit of thought, personal relations, &c. of the author 
by whom it professes to have been written, so that 
everything may militate for, and nothing militate 
against, its authenticity. 

" But if our criticism from the internal grounds But onmi- 
alone be, on the one hand, impotent to establish, it is, disprove" 
on the other, omnipotent to disprove. For it is suffi- 
cient to show that a writing is in essential parts, that 
is, parts which cannot be separated from the whole, 
in opposition to the known manners, institutions, 
usages, &c., of that people with which it would, and 
must, have been in harmony, were it the product of 
the writer whose name it bears ; that, on the contrary, 
it bears upon its face indications of another country 
or of a later age ; and, finally, that it is at variance 



196 LECTURES ON LOGIC. 

LECT. with, the personal circumstances, the turn of mind, 

XXXIV 

— '- and the pitch of intellect, of its pretended author. 

And here it is to be noticed, that these grounds are 
only relatively internal ; for we become aware of 
them originally only through the testimony of others, 
that is, through external grounds." '^ 

b. External In regard to the External Grounds : — they, as I 

Grounds. ^ . . , . , . . , . "^ . 

said, consist m the testimony, direct or indirect, given 
to the authenticity of the writing in question by other 
works of a competent antiquity. This testimony may 
be contained either in other and admitted writino;s of 
the supposed author himself ; or in those of contem- 
porary writers ; or in those of writers approximat- 
ing in antiquity. This testimony may also be given 
either directly, by attribution of the disputed writing 
by title to the author ; or indirectly, by quoting as 
his, certain passages which are to be found in it. On 
this subject it is needless to go into detail, and it is 
hardly necessary to observe, that the proof of the 
authenticity is most complete when it proceeds upon 
the internal and external grounds together. I, there- 
fore, pass on to the Criticism of Integrity. ^ 
2. Criticism " Wlicu thc authenticity of an ancient work has 
been established on external grounds, and been con- 
firmed on internal, the Integrity of this writing is 
not therewith proved ; for it is very possible, and in 
ancient writings indeed very probable, that particular 
passages are either interpolated or corrupted. The 
authenticity of particular passages is to be judged of 
precisely by the same laws, which regulate our criti- 
cism of the authenticity of the whole work. The proof 
most pertinent to the authenticity of particular pas- 

o Esser, Logik, § 158-160.— Ed. /3 See Esser, Logik, §§ 161, 162.— Ed. 



LECTURES ON LOGIC. 197 

sao^es is drawn — 1° From tlieir ackDOwledsment by lect. 

. a J XXXIV 

the author himself in other, and these unsuspected, 1 

works ; 2°, From the attribution of them to the author 
by other writers of competent information ; and, 3°, 
From the evidence of the most ancient MSS. On the 
other hand, a passage is to be obelized as spurious, — 
1°, When found to be repugnant to the general relations 
of time and place, and to the j^ersonal relations of the 
author ; 2°, When wanting in the more ancient codices, 
and extant only in the more modern. A passage is 
suspicious, when any motive for its interpolation is 
manifest, even should we be unable to establish it as 
spurious. The differences which different copies of a 
writing exhibit in the particular passages, are called 
various readings (varice lectiones or lectiones vari- 
antes). Now, as of various readings one only can be 
the true, while they may all very easily be false, the 
problem which the criticism of Integrity proposes to 
solve is,— How is the genuine reading to be made out, 
— and herein consists what is technically called the 
Recension, more properly the Emendation, of the text. 

"The Emendation of an ancient author may be of Emendation 

• of tilG text 

two kinds ; the one of which may be called the His- -of two 
torical, the other the Gonjectwxd. The former of these Historical' 
founds upon historical data for its proof ; the latter, jecturai. 
again, proceeds on grounds which lie beyond the sphere 
of historical fact, and this for the very reason that his- 
torical fact is found incompetent to the restoration of 
the text to its original integrity. The historical emen- 
dation necessarily precedes the conjectural, because the 
object itself of emendation is wholly of an historical 
character, and because it is not permitted to attempt 
any other than an emendation on historical grounds, 



198 LECTUKES ON LOGIC. 

LECT. until, from these very 2;rounds themselves, it be shown 

XXXIV . 

1 that the restitution of the text to its original integrity 

Historical cauuot be historically accomplished. Historical Emen- 

kb^ds— ^^tion is again of two kinds, according as its judgment 

External procccds ou extcmal or on internal ^'rounds. It founds 

and Inter- ^ o 

^'^i- upon external grounds, when the reasons for the truth 

or falsehood of a reading are derived from testimony ; 
it founds upon internal grounds, wdien the reasons for 
the truth or falsehood of a reading are derived from 
the writing itself. Historical emendation has thus a 
twofold function to perform, (and in its application to 
practice, these must always be performed in conjunc- 
tion), viz., it has carefully to seek out and accurately 
to weigh both the external and internal reasons in sup- 
port of the reading in dispute. Of external grounds 
the princijjal consists in the confirmation afforded by 
MSS., by printed editions which have immediately 
emanated from MSS., by ancient translations, and by 
passages quoted in ancient authors. The internal 
grounds are all derived either from the form, or from 
the contents, of the work itself. In reference to the 
form, — a reading is probable, in proportion as it cor- 
responds to the general character of the language pre- 
valent at the epoch when the work was written, and 
to the peculiar character of the language by which the 
author himself was distinguished. In reference to the 
contents, — a reading is probable, when it harmonises 
with the context, that is, when it concurs with the 
other words of the particular passage in which it 
stands, in affording a meaning reasonable in itself, and 
conformable with the author's opinions, reasonings, 
and general character of thought.'"' 

a Esaer, Loijlk, § 163.— Ed. 



LECTURES ON LOGIC. 199 

It frequently happens, however, that, notwithstand- lect. 
ing the uniformity of MSS. and other external sub- — ^ — 1 
sidia, a reading cannot be recognised as genuine. In imemia-'^'^' 
this case, it must be scientifically shown from the ^'°'^' 
rules of criticism itself, that this lection is corrupt. 
If the demonstration thus attempted be satisfactory, 
and if all external subsidia have been tried in vain, 
the critic is permitted to consider in what manner the 
corrupted passage can be restored to its integrity. 
And here the conjectural or divinatory emendation 
comes into play ; a process in which the power and 
eflficiency of criticism and the genius of the critic are 
principally manifested," " 

So much for Criticism, in its applications both to 
the Authenticity and to the Integrity of Writings. 
We have now to consider the general rules by which 
Interpretation, that is, the scientific process of ex- 
pounding the Meaning of an author, is regulated. 

" By the Art of Interpretation, called likewise techni- it. inter- 
cally Hei^meneutic or Exegetic, is meant the comple- 
ment of logical laws, by which the sense of an ancient 
writing is to be evolved. Hermeneutic is either Gen- General and 

Special. 

eral or Special. General, when it contains those laws 
which apply to the interpretation of any writing 
whatever ; Special, when it comprises those laws by 
which writings of a particular kind are to be ex- 
pounded. The former of these alone is of logical 
concernment. The problem proposed for the Art of 
Interpretation to solve, is, — How are we to proceed 
in order to discover from the words of a writing that 
sole meaning which the author intended them to 
convey \ In the interpretation of a work, it is not, 

a Esser, Log tic, § 166. — Ed. [Par- Geiiuensis, Ars Logico-Critica, L. iv. 
rhasiana, i. 359-365, 2d ed. 1701. c. vi. ct seq.] 



200 LECTURES ON LOGIC. 

LECT. therefore, enough to show in what signification its 

XXXIV ... 

'- words may be understood ; for it is required that we 

show in what signification they must. To the execu- 
tion of this task two conditions are absolutely neces- 
sary ; 1°, That the interpreter should be thoroughly 
acquainted with the language itself in general, and 
with the language of the writer in particular ; and 2°, 
That the interpreter should be familiar with the sub- 
jects of which the writing treats. But these two 
requisites, though indispensable, are not of themselves 
sufiicient. It is also of importance that the expo- 
sitor should have a competent acquaintance with the 
author's personal circumstances and character of 
thought, and with the history and spirit of the age 
and country in which he lived. In regard to the inter- 
pretation itself ; — it is to be again observed, that as a 
writer could employ expressions only in a single sense, 
so the result of the exposition ought to be not merely 
to show what meaning may possibly attach to the 
doubtful terms, but what meaning necessarily must. 
When, therefore, it appears that a passage is of doubt- 
ful import, the best preparative for a final determin- 
ation of its meaning is, in the first place, to ascertain 
in how many different significations it may be con- 
strued, and then, by a process of exclusion, to arrive 
at the one veritable meaning. When, however, the 
obscurity cannot be removed, in that case it is the 
duty of the exjDositor, before abandoning his task, to 
evince that an interpretation of the passage is, with- 
out change, absolutely or relatively impossible. 
Sources of " As to the sourccs from whence the Interpretation 
^nwprea ^^ ^^ ^^ drawu, — tlicsc are three in aU, — viz., 1°, The 
Tractus literarum, the words themselves, as they ap- 
pear in MSS. ; 2°, The context, that is, the passage 



LECTURES ON LOGIC. 201 

in immediate connection with the doubtful term ; 3°, lect. 

Parallel or analogous passages in the same, or in other, '~ 

writings." " How the interpretation drawn from these 
sources is to be applied, I shall not attempt to detail ; 
but pass on to a more generally useful and interesting 
subject. 

So much for Experience or Observation, the first Specuiatiou 
mean of scientific discovery, that, viz., by which we Means of 

1 -, I . , . , Knowledge. 

apprehend what is presented as contingent phseno- 
mena, and by whose processes of Induction and 
Analogy we carry up individual into general facts. 
We have now to consider the other Mean of scientific 
discovery, that, viz, by which, from the phsenomena 
presented as contingent, we separate what is really 
necessary, and thus attain to the knowledge, not of 
merely generalised facts, but of universal laws. This 
mean may, for distinction's sake, be called Specula- 
tion, and its general nature I comprehend in the fol- 
lowing paragraph. 

IF CXI. When the mind does not rest con- Par. cxi. 
tented with observing and classifying the objects —as a 

(, . . ■, 1 n • 1 • nieans of 

01 its experience, but, by a reilective analysis. Knowledge. 
sunders the concrete wholes presented to its 
cognition, throws out of account all that, as con- 
tingent, it can think away from, and concen- 
trates its attention exclusively on those elements 
which, as necessary conditions of its own acts, it 
cannot but think : — by this process it obtains the 
knowledge of a certain order of facts, — facts of 
Self-consciousness, which, as essential to all Ex- 
perience, are not the result of any ; constituting 

o Eeser, LogiJc, § 167.— Ed. [Cf. Snell, Loyil-, p. ii. § 6, p. 200.] 



202 LECTURES ON LOGIC. 

LECT. ill truth tlie Laws by which the possibility of our 

^^^^^- cognitive functions is determined. This process, 

by which we thus attain to a discriminative 
knowledge of the Necessary, Native, and, as they 
are also called, the Noetic, Pure, a ijriori, or 
Transcendental, Elements of Thought, may be 
styled Speculative Analysis, Analytic Specula- 
tion, or Speculation simply, and is carefully to be 
distinguished from Induction, with which it is 
not unusually confounded. 



tion 



Expiica- " The empirical knowledge of which we have 
hitherto been speaking, does not, however varied and 
extensive it may be, suffice to satisfy the thinking 
mind as such ; for our empirical knowledge itself 
points at certain higher cognitions from which it may 
obtain completion, and which are of a very different 
character from that by which the mere empirical cog- 
nitions themselves are distinguished. The co2;nitions 
are styled, among other names, by those of noetic, 
pure, or rational, and they are such as cannot, though 
manifested in experience, be derived from experience ; 
for, as the conditions under which experience is pos- 
sible, they must be viewed as necessary constituents 
of the nature of the thinking principle itself. Philo- 
sopbers have indeed been found to deny the reality of 
such cognitions native to the mind ; and to confine 
the whole sphere of human knowledge to the limits of 
experience. But in this case philosophers have over- 
looked the important circumstance, that the acts, that 
is, the apprehension and judgment, of experience, are 
themselves impossible, except under the supposition of 
certain potential cognitions previously existent in the 
thinking subject, and which become actual on occa- 



LECTURES ON LOGIC. 203 

sion of an obiect beina; presented to tlie external or lect. 

... xxxiv 
internal sense. As an example of a noetic cognition, 1 1 



the following propositions may suffice : — An object 
and all its attributes are convertible ; — All that is 
has its sufficient cause. The principal distinctions of Principal 
Empirical and Rational Knowledges, or rather Em-ofEmpiri- 
pirical and Noetic Cognitions, are the following : — 1°, Noetic Cog- 
Empirical cognitions originate exclusively in experi-°'^*^ 
ence, whereas noetic cognitions are virtually at least 
before or above all experience, — all experience being 
only possible through them. 2°, Empirical cognitions 
come piecemeal and successively into existence, and 
may again gradually fade and disappear ; whereas 
noetic cognitions, like Pallas armed and immortal from 
the head of Jupiter, spring at once into existence, com- 
plete and indestructible. 3°, Empirical cognitions find 
only an application to those objects from which they 
were originally abstracted, and, according as things ob- 
tain a different form, they also may become differently 
fashioned ; noetic cognitions, on the contrary, bear 
the character impressed on them of necessity, uni- 
versality, sameness. Whether a cognition be empirical 
or noetic, can only be determined by considering 
whether it can or cannot be presented in a sensible 
perception ; — whether it do or do not stand forward 
clear, distinct, and indestructible, bearing the stamp 
of necessity and absolute universality. The noetic 
cognitions can be detected only by a critical analysis 
of the mental pheenomena proposed for the purpose of 
their discovery;"" and this analysis may, as I have 
said, be styled Speculation, for want of a more appro- 
priate appellation. 

a Esser, Logil-, § 171. — Ed. 



201 



LECTURES ON LOGIC. 



LECTURE XXXV. 

MODIFIED METHODOLOGY. 

SECTION I. — OF THE ACQUISITION OF KNOWLEDGE. 

III. COMMUNICATION OF KNOWLEDGE. A. INSTRUCTION 

ORAL AND WRITTEN. B. CONFERENCE 

DIALOGUE AND DISPUTATION. 



LECT. I NOW 0^0 on to the last Mean of Acquiring and Per- 
_1^^ fecting our knowledge ; and commence with the fol- 
lowing paragraph : — 



Par. OXII, 

The Cora- 
municaliou 
of Thought, 
— as a 
means of 
Acquiring 
and Per- 
fecting 
Knowledge. 



H CXI I. An important mean for the Acqui- 
sition and Perfecting of Knowledge is the Com- 
munication of Thought. Considered in general, 
the Communication of thought is either One-sided, 
or Mutual. The former is called Instruction 
{institutio), the latter Conference {collocutio) ; 
but these, though in theory distinct, are in prac- 
tice easily combined. Instruction is again either 
Oral or Written ; and Conference, as it is inter- 
locutory and familiar, or controversial and solemn, 
may be divided into Dialogue [colloquium, dia- 
logus), and Disputation ( disputatio, concertatio)- 
The Communication of thought in all its forms 
is a means of intellectual improvement, not only 



LECTURES ON LOGIC. 205 

to him who receives, but to him who bestows, lect. 
information ; in both relations, therefore, it ought - 



to be considered, and not, as is usually done, in 
the latter only." 

In illustrating this paragraph, I shall commence Expiica- 
with the last sentence, and, before treating in detail 
of Instruction and Conference, as means of extendino- 
the limits of our knowledge by new acquisitions de- 
rived from the communication of others, I shall en- The Com- 
deavour to show, that the Communication of thought of™hougiu 
is itself an important mean towards the perfecting of unt'^ean 
knowledge in the mind of the communicator himself. p°eXcting^ 
In this view, the communication of knowledge is like LdgeTiTthe 
the attribute of mercy, twice blessed, — " blessed to ™mmunicr- 
him that gives and to him that takes ;" in teaching 
others we in fact teach ourselves. 

This view of the reflex effect of the communication 
of thought on the mind, whether under the form of 
Instruction or of Conference, is one of high importance, 
but it is one w^hich has, in modern times, unfortunately 
been almost wholly overlooked. To illustrate it in 
all its bearings would require a volume, — at present 
I can only contribute a few hints towards its expo- 
sition. 

Man is, by an original tendency of his nature, de- Man natu- 
termined to communicate to others what occupies his mined to 



communica- 



thoughts, and by this communication he obtains ation. 
clearer understanding of the subject of his cogitations 
than he could otherwise have compassed. This fact This fact 

- . , , P -,-., T 1 7^ noticed by 

did not escape the acuteness oi rlato. In tne Jrvota- piato. 
goras, — " It has been well," says Plato (and he has 

a Cf. Knig, Logik, § 181 et seq. — Ed. 



20G LECTURES ON LOGIC. 

LECT. sundry passages to the point), — " It lias been well, I 
think, observed by Homer — 



' Through mutual intercourse and mutual aid, 
Great deeds are done and great discoveries made ; 
The wise new wisdom on the wise bestow, 
Whilst the lone thinker's thoughts come slight and slow.' o 

For in company we, all of us, are more alert, in deed 
and word and thought. And if a man excogitate 
aught hy himself, forthwith he goes about to find some 
one to whom he may reveal it, and from vAom he may 
obtain encouragement, aye and until his discovery be 
completed!'^ The same doctrine is maintained by 

Aristotle. Aristotlc, and illustrated by the same quotation ; "^ 
(to which, indeed, is to be referred the adage, — "Unus 

Themistius. homo, uullus liomo.") — " We rejoice," says Themistius, 
" in hunting truth in company, as in hunting game." ^ 

Luciiius. Lucilius, — " Scire est nescire, nisi id me scire alius 
scierit ; ^ — paraphrased in the compacter, though far 

Persius. inferior, verse of Persius, — " Scire tuum nihil est, nisi 

Cicero. tc sciro hoc sciat alter."^ — Cicero's Cato testifies to 
the same truth : — " Non facile est invenire, qui quod 

Seneca. sciat ipsc, uou tradat alteri." "^ And Seneca : — " Sic 
cum hac exceptione detur sapientia, ut illam inclusam 
teneam nee enunciem, rejiciam. Nullius boni, sine 
socio, jucunda possessio est." ^ 

" Condita tabescit, vulgata scientia crescit." * 



a Altered from Pope's Homer, Book f I. 27. — Ed. 

X. 265. 7) Cato apud Cicero, De Fin., iii. 

fi Protag., p. 348. Compare Lee- c. 20, § 66. 

tures on Metaphysics, i. p. 376. B Seneca, Ep., vi. 

7 Eth. Nlc., viii. 1. t Quoted also in Discussions, p. 778. 

5 Orat., xxi. Explorator aut Philo- This line appears to have been taken 
sopJtus, Orationes, p. 254, ed. Harduin, from a small volume, entitled, Car- 
Paris, 1684. — Ed. minum Prorerbialium Loci Communes, 

€ Fragm., 25, in the Bipont edition p. 17, Lond. 1583 ; but the author is 

of Persius and Juvenal, p. 176. — Ed. not named. — Ed. 



LECTURES ON LOGIC. 207 

" In hoc gaudeo aliquid discere, ut doceam : nee me lect. 

uUa res delectabit, licet eximia sit et salutaris, quam 11 1 

mihi uni, sciturus sim." '^ " Ita non solum ad discen- 
dum propensi snmus, verum etiam ad docendum,"/^ 

The modes in which the Communication of thought Modes m 
is conducive to the perfecting of thought itself, are munication 

_ - . _ . _ . ^ is conducive 

two ; lor the mind may be determined to more ex- to the Per- 
alted energy by the sympathy of society, and by the Thought 
stimulus of opposition ; or it may be necessitated 
to more distinct, accurate, and orderly thinking, as 
this is the condition of distinct, accurate, and orderly 
communication. Of these the former requires the 
presence of others during the act of thought, and is, 
therefore, only manifested in oral instruction or in 
conference ; whereas the latter is operative both in 
our oral and in our written communications. Of these 
in their order. 

In the first place, then, the influence of man on i. By red- 
man in reciprocally determining a higher energy oflCTmLing' 
the faculties, is a phsenomenon sufiiciently manifest. euerVof 
By nature a social being, man has powers which aretiel""^" 
relative to, and, consequently, find their development L mpTth^^ 
in, the company of his fellows ; and this is more par- 
ticularly shown in the energies of the cognitive facul- 
ties. "As iron sharpeneth iron," says Solomon, "so a 
man sharpeneth the understanding of his friend."'^ 
This, as I have said, is efiected both by fellow-feeling 
and by opposition. We see the efiects of fellow-feel- 
ing, in the necessity of an audience to call forth the 
exertions of the orator. Eloquence requires numbers ; 
and oratory has only flourished where the condition 

o Seneca, Epist., vi. — Ed. rised vei'sion is, countenance of his 

j3 Cicero, De Fin. iii. 20. — Ed. friend. Compare Lectures on Meta- 

y Proverbs, xxvii. 17. The autho- physics, vol. i. p. 376. — Ed. 



208 LECTURES ON LOGIC, 

LECT. of large audiences has been supplied. But opposition 
is perhaps still more powerful than mere sympathy in 



dpposiUon. calling out the resources of the intellect 
Plutarch, In the mental as in the material world, action and 
reaction are ever equal ; and Plutarch'^ well ob- 
serves, that as motion would cease were contention 
to be taken out of the physical universe, so pro- 
gress in improvement would cease were contention 
taken out of the moral ; vroXe/xos olttolvtcop rraTi/jp.^ 
Scaiiger, " It is maintained," says the subtle Scaliger, " by 

Vives, that we profit more by silent meditation than 
by dispute. This is not true. For as fire is elicited 
by the collision of stones, so truth is elicited by the 
collision of minds, I myself (he adds) frequently 
meditate by myself long and intently ; but in vain ; 
unless I find an antagonist, there is no hope of a 
successful issue. By a master we are more excited 
than by a book ; but an antagonist, whether by 
his pertinacity or his wisdom, is to me a double 
master," ''' 
2, By im- But, iu tlic sccoud placc, the necessity of communi- 
nece^lty of catlug a plccc of kuowledgo to others, imposes upon 

obtaining a .i ,, f*ii"* pn • r 

fuller con- Hs thc ueccssity 01 obtammg a luller consciousness oi 
of'know-^ that knowledge for ourselves. This result is to a cer- 
ouileives. taiu extcut secured by the very process of clothing our 
cogitations in words. For speech is an analytic pro- 
cess ; and to express our thoughts in language, it is 
requisite to evolve them from the implicit into the 
explicit, from the confused into the distinct, in order 
to bestow on each part of the organic totality of a 
thought its precise and appropriate symbol. But to 

a Vifa Agesilai, Opera, 1599, vol. i. Philos., i. p. 158. — Ed. 
p. 598. — Ed, 7 E.vercit., f. 420. [For a criticism 

Hei-aclitus. Cf. Plutarch, De Is. of Sealiger's remark as regards Vives, 

tt 0$ir., p. 370. Brandis, Gesch. der see Discussions, p. 773. — Ed.] 



LECTURES ON LOGIC. 209 

do this is in fact only to accomplish the first step lect. 

XXXV 

towards the perfecting of our cognitions or thoughts. ^ 

But the communication of thouo;ht, in its hio-her ap- influence of 

T • . r 1 1 • 1 • Composi. 

plications, imposes on us far more than this ; and m tion and 

1 • • • 1 •^^ 1 r> • ^ • n Instruction 

SO doing it reacts with a still more beneficial mfiuence inperfecting 

11' r» 1 • 1 • n 1 "^^ Know- 

on our habits of thinking, buppose that we are not ledge. 

merely to express our thoughts as they spontaneously 
arise; suppose that we are not merely extemporane- 
ously to speak, but deliberately to write, and that 
what we are to communicate is not a simple and easy, 
but a complex and difficult, matter. In this case, no 
man will ever fully understand his subject who has 
not studied it with the view of communication, while 
the power of communicating a subject is the only 
competent criterion of his fully understanding it. 
"When a man," says Godwin, "writes a book of method- Godwin 
ical investigation, he does not write because he under- 
stands the subject, but he understands the subject 
because he has written. He was an uninstructed tyro, 
exposed to a thousand foolish and miserable mistakes, 
when he began his work, compared with the degree 
of proficiency to which he has attained when he has 
finished it. He who is now an eminent philosopher, 
or a sublime poet, was formerly neither the one nor 
the other. Many a man has been overtaken by a pre- 
mature death, and left nothing behind him but com- 
positions worthy of ridicule and contempt, who, if he 
had lived, would perhaps have risen to the highest 
literary eminence. If we could examine the school 
exercises of men who have afterwards done honour to 
mankind, we should often find them inferior to those 
of their ordinary competitors. If we could dive into 
the portfolios of their early youth, we should meet 
with abundant matter for laughter at their sense- 

VOL. IL 



210 



LECTURES ON LOGIC. 



LECT. 
XXXY. 



Aristotle. 



less iDcongruities, and for contemptuous astonish- 
ment."" 

" The one exclusive sign," says Aristotle, " that a 
man is thoroughly cognisant of anything is that he is 
able to teach it;"^ and Ovid, — ^ 

" Quodque pariun novit nemo clocere potest." 

In this reactive effect of the communication of 
knowledge in determining the perfection of the know- 
ledge communicated, originated the scholastic maxim 
Doce lit discas, — a maxim which has unfortunately 
been too much overlooked in the schemes of modern 
education. In former ages, teach that you may learn, 
always constituted one at least of the great means of 
intellectual cultivation. "To teach," says Plato, "is 
the way for a man to learn most and best."^ "Hom- 
ines dum decent discunt," says Seneca.^ " In teach- 

ciementof iug," says Clement of Alexandria,^ "the instructor often 
' " learns more than his pupils." " Disce sed a doctis ; 

Dionysius indoctos ipse doceto," is the precept of Dionysius Cato ;'' 
and the two following were maxims of authority in 
the discipline of the middle ages. The first — 

, " Multa rogare, rogata tenere, retenta docere, 

Haec tria, discipulum faciunt superare magistrum." & 

The second — 

" Discere si quaeris doceas ; sic ijise doceris ; 
Nam studio tali tibi proficis atque sodali." ' 



Plato. 



Seneca. 



a Enquirer, Part i. Essay iv. pp. 
23, 24, ed. 1797.— Ed. 

/3 Metajjhys., i. L Quoted in Z);s- 
cussions, p. 765. — Ed. 

7 Tristia, ii. 348.— Ed. 

8 Pseudo-Plato, Epinomis, p. 989. 
—Ed. 

e Epist, 7.— Ed. 

f Stromata, lib. i. p. 275, ed. 
Sylb. : A.i5dcrKot3V ns fiavOdvei irXelov, 
Kol \4yuiv ffwaKpoarai iroWaKts toIs 



iiraKOvovffiv avrov. — Ed. 

V IV. 29.— Ed. 

d [Crenius, p. 581.] [OabrieViv 
NaudcBi Syntagma de Studio Liberali, 
Included in tbe Consilia et Methodi 
Aureoi studiorum optime instituendo- 
rum, collected by Th. Crenius, Kot- 
terdam, 1G92. The lines are quoted 
as from an anonymous author. — 
Ed.] 

I Given without author's name, in 



LECTURES ON LOGIC. 211 

Tliis truth is also well enforced by the Qjreat Vives. lect. 

XXXV 

" Doctrina est traditio eorum quae quis novit ei qui 



non novit. Disciplina est illius traditionis acceptio ; ^'^^^' 
nisi quod mens accipientis impletur, dantis vero non 
exhauritur, — imo communicatione augetur eruditio, 
sicut ignis, motu atque agitatione. Excitatur enim 
ingenium, et discurrit per ea quae ad prsesens nego- 
tium pertinent ; ita invenit atque excudit multa, et 
quae in mentem non veniebant cessanti, docenti aut 
disserenti occurrunt, calore acuente vigorem ingenii. 
Idcirco, nihil est ad magnam eruditioneni perinde 
conducens, ut docere."" The celebrated logician, Dr Sanderson. 
Robert Sanderson, used to say : " I learn much from 
my master, more from my equals, and most of all 
from my disciples."^ 

But I have occupied perhaps too much time on the influence 
influence of the communication of knowledge on those muuication 

,,.. , ^^.. -of Know- 

by whom it IS made ; and shall now pass on to the lodge on 

consideration of its influence on those to whom it is whom it is 

addressed. And in treating of communication in 

this respect, I shall, in the first place, consider it 

as One-sided, and, in the second, as Eeciprocal or 

Bilateral. 

The Unilateral Communication of knowledge, or i. instmc- 
Instruction, is of two kinds, for it is either Oral orand'writ- 
Written ; but as both these species of instruction pro- 
pose the same end, they are both, to a certain extent, 
subject to the same laws. 

Oral and Written Instruction have each their pecu- 
liar advantages. 

In the first place, instruction by the living voice 

the Carmimim Proverbialum Loci fi [Reason and Judgment, or Spe- 

Communes, Loncl. 1583, p. 17. See cial Remarks of the Life of the Re- 

above, p. 206, note i. — Ed. noioned Dr Sanderson, p. 10. Lon- 

a De Anima, p. 89. don : 1663,] 



212 



LECTURES ON LOGIC. 



LECT. 
XXXV. 

Oral in- 
struction, 
— its ad- 
vantages, 
a. More 
natural, 
therefore 
more im- 
pressive. 
Theophras- 
tus. 

Younger 
Pliny. 



Valerius 
Maximi.s. 



St Jerome. 



b. Less per- 
manent, 
therefore 
more at- 
tended to. 



c. Hearing 
a social act, 



lias this advantage over that of books, that, as more 
natural, it is more impressive. Hearing rouses the 
attention and keeps it alive far more effectually than 
reading. To this we have the testimony of the most 
competent observers. " Hearing," says Theophrastus," 
" is of all the senses the most pathetic," that is, it is 
the sense most intimately associated with sentiment 
and passion. " Multo magis," says the younger 
Pliny, " multo magis viva vox afficit. Nam, licet 
acriora sunt quae legas, altius tamen in animo sedent 
quse pronuntiatio, vultus, habitus, gestus etiam dicen- 
tis adfigit." ^ 

" Plus prodest," says Valerius Maximus, " docentem 
audire, quam in libris studere; quia vehementior fit 
impressio in mentibus audientium, ex visu doctoris et 
auditu, quam ex studio et libro."''^ 

And St Jerome — " Habet nescio quid latentis ener- 
gise viva vox; et in aures discipuli de doctoris ore 
transfusa, fortius sonat."^ 

A second reason why our Attention (and Memory 
is always in the ratio of Attention) to things spoken 
is greater than to things read, is that what is written 
we regard as a permanent possession to which we can 
always recur at pleasure; whereas we are conscious 
that the "winged words" are lost to us for ever, if we 
do not catch them as they fly. As Pliny hath it : — 
"Legendi semper est occasio; audiendi non semper."^ 

A third cause of the superior efiicacy of oral in- 



a OvK Uv arjScos 5' ol/xai ae Trpoca- 
Kovcrai irepl ttjs aKovffTiKTJs alffdrjfffwi, 
^v 6 @f6(ppa<TTos iraQrjTLKiiiraTriv elvai 
<pr)<rl iracrwv. Plutarch, De Auditione, 
sub init. — Ed. 

6 Ejjist., ii. 3.— Ed. 

7 [Thomas Hiberiiicus, p. 330.] 
[The above passage is quoted as from 



Valerius, lib. viii., in the Flores of 
Thomas Hibernicus, and in the An- 
thologia of Langius, under the article 
Doctrina. It is not, however, to be 
found in that author. — Ed. ] 

S Epist, ciii, OjJera, Antv. 1579, 
tom. iii. p. 337.— Ed. 

e Ujjist., ii. 3 Ed. 



LECTURES ON LOGIC. 218 

struction is that man is a social animal. He is thus lect. 
naturally disposed to find pleasure in society, and in ^ ^ 



the performance of the actions performed by those 
with whom he consorts. But reading is a solitary, 
hearing is a social, act. In reading, we are not deter- 
mined to attend by any fellow-feeling with others 
attending; whereas in hearing, our attention is not 
only engaged by our sympathy with the speaker, but 
by our sympathy with the other attentive auditors 
around us. 

Such are the causes which concur in rendering Menage 
Oral Instruction more effectual than Written. "M. 
Varillas," says Menage, (and Varillas was one of the 
most learned of modern historians, — and Menage one 
of the most learned of modern scholars), " M. Varillas 
himself told me one day, that of every ten things 
he knew, he had learned nine of them in conversation. 
I myself might say nearly the same thing."" 

On the other hand, Reading, though only a substi- Reading — 
tute for Oral Instruction, has likewise advantages lages.' 
peculiar to itself. In the first place, it is more easily I'^lly'^^ 
accessible. In the second, it is more comprehensive ^'"''^j^'^g^^' 
in its sphere of operation. In the third, it is not ^?™p^''''^°' 
transitory with the voice, but may ao;ain and ap'ain c. More 

^ _ ./ o o permanent. 

be taken up and considered, so that the object of the 
instruction may thus more fully be examined and 
brought to proof. It is thus manifest, that oral and 
written instruction severally supply and severally sup- 
port each other ; and that, where this is competent, 
they ought always to be employed in conjunction. 
Oral instruction is, however, in the earlier stages 
of education, of principal importance ; and written 
ought, therefore, at first only to be brought in as a 

a Menagiana, torn. iv. p. Ill, ed. 1715. ^Ed. 



214! LECTUKES ON LOGIC. 

LECT. subsidiary. A neglect of the oral instruction, and an 

XXXV •/ cj 

L exclusive employment of the written, — the way in 

which those who are self-taught (the autodidacti) 
obtain their education, — for the most part betrays its 
one-sided influence by a contracted cultivation of the 
intellect, with a deficiency in the power of communi- 
cating knowledge to others. 

Oral instruction necessarily supposes a speaker and 
a hearer ; and written instruction a writer and a 
reader. In these, the capacity of the speaker and of 
the writer must equally fulfil certain common requi- 
sites. In the first place, they should be fully masters 
of the subject with which their instruction is conver- 
sant ; and in the second, they should be able and 
willing to communicate to others the knowledge which 
they themselves possess. But in reference to these 
several species of instruction, ther^ are various special 
rules that ought to be attended to by those who would 
reap the advantages they severally afford. I shall 
commence with Written Instruction, and comprise the 
rules by which it ought to be regulated, in the follow- 
ing paragraph. 

Par.cxiii. H CXIII. In regard to Written Instruction, 

*» ri ttcii 

Instruction, and its profitable employment as a means of in- 

aud its em- j_ n j. i • i • i 

pioyment tcllectuaJ improvcmcut, there are certain rules 

ofinteiiec- which ouglit to bc observed, and which to2;ether 

pr'ovement. constituto thc Propcr Method of Eeading. These 

may be reduced to three classes, as they regard, 

1°, The Quantity, 2°, The Quality, of what is to be 

read, or, 3°, The Mode of reading what is to be read. 

I. As concerns the Quantity of what is to be 

read, there is a single rule,— Read much, but 

not many works (multum non multa). 



LECTURES ON LOGIC. 215 

II. As concerns the Quality of what is to be lect. 

\xxv 
read, — there may be given five rules. 1°, Select '- 

the works of principal importance, estimated by 
relation to the several sciences themselves, or to 
your particular aim in reading, or to your indi- 
vidual disposition and wants. 2°, Eead not the 
more detailed works upon a science, until you 
have obtained a rudimentary knowledge of it in 
general. 3°, Make yourselves familiar with a 
science in its actual or present state, before you 
proceed to study it in its chronological develop- 
ment. 4°, To avoid erroneous and exclusive 
views, read and compare together the more im- 
portant works of every sect and party. 5°, To 
avoid a one-sided development of mind, combine 
with the study of works which cultivate the 
Understanding, the study of works which culti- 
vate the Taste. 

III. As concerns the Mode or Manner of read- 
ing itself, there are four principal rules. 1°, 
Read that you may accurately remember, but 
still more, that you may fully understand. 2°, 
Strive to compass the general tenor of a work, 
before you attempt to judge of it in detail. 3°, 
Accommodate the intensity of the reading to the 
importance of the work. Some books are, there- 
fore, to be only dipped into; others are to be run 
over rapidly ; and others to be studied long and 
sedulously. 4°, Eegulate on the same principle 
the extracts which you make from the works you 
read." 

a. Cf. Krug, Logih, § 180.— Ed. § 53, p. 196 ; 1832. Magirus Flori- 
[Fischaber, Logik, p. 188, ed. 1818. legium, v. Lectio.'] 
Scheidler, Grundriss der Hodegctih, 



216 



LECTUHES ON LOGIC. 



LECT. 
XXXV. 

Explica- 
tion. 

I. Quantity 
to be read. 
Rule. 



Solomon, 

Quintilian. 

Younger 

Pliny. 

Seneca. 

Luther 
quoted. 



Sanderson. 



I. In reference to the head of Quantity, the single 
rule is — Eead much, but not many works. Though 
this golden rule has risen in importance, since the 
world, by the art of printing, has been overwhelmed 
by the multitude of books, it was still fully recog- 
nised by the great thinkers of antiquity. It is even 
hinted by Solomon, when he complains that " of mak- 
ing many books there is no end."" By Quintilian, 
by the younger Pliny, and by Seneca, the maxim — 
" multum legendum esse, non multa " — is laid down 
as the great rule of study.^ " All," says Luther 
in his Table Talk,'^ " who would study with advan- 
tage in any art whatsoever, ought to betake them- 
selves to the reading of some sure and certain books 
oftentimes over; for to read many books produceth 
confusion, rather than learning, like as those who 
dwell everywhere, are not anywhere at home." He 
alludes here to the saying of Seneca, " Nusquam est 
qui ubique est."^ "And like as in society, we use 
not daily the community of all our acquaintances, 
but of some few selected friends, even so likewise 
ought we to accustom ourselves to the best books, 
and to make the same familiar unto us, that is, to 
have them, as we use to say, at our lingers' ends." 
The great logician, Bishop Sanderson, to whom I for- 
merly referred, as his friend and biographer Isaac A¥al- 
ton informs us, said " that he declined reading many 
books ; but what he did read were well chosen, and 
read so often that he became very familiar with them. 
They were principally three, — Aristotle's Rhetoric, 
Aquinas's Secunda Secundce, and Cicero, particularly 



I 



a Eccles. xii. 12.— Ed. 

/3 Quintilian, x. 1, 59. Pliny, 
Ep., vii. 9. Seneca, De TranquUl. 
Animi, c. 9; Ejnst., 2, 45. — Ed. 



7 No. DCCCXLiv. Of Learned Men. 
-Ed. 

8 Ejnst., ii.— Ed. 



LECTUEES ON LOGIC. 217 

his Offices.""' The great Lord Burleigh, we are told lect. 
by his biographer, carried Cicero De Officiis, with 



Aristotle's Rhetoric, always in his bosom ; these being J^?^^ ^^■ 
complete pieces, " that would make both a scholar and 
an honest man." " Our age," says Herder, " is the Herder. 
reading age ; " and he adds, " it would have been 
better, in my opinion, for the world and for science, 
if, instead of the multitude of books which now over- 
lay us, we possessed only a few works good and ster- 
ling, and which, as few, would, therefore, be more 
diligently and profoundly studied."^ I might quote 
to you many other testimonies to the same effect ; 
but testimonies are useless in support of so manifest 
a truth. 

For what purpose, — with what intent, do Ave read 1 Eud of 
We read not for the sake of reading, but we read to 
the end that we may think. Heading is valuable 
only as it may supply to us the materials which 
the mind itself elaborates. As it is not the largest 
quantity of any kind of food, taken into the stomach, 
that conduces to health, but such a quantity of such 
a kind as can be best digested ; so it is not the 
greatest complement of any kind of information that 
improves the mind, but such a quantity of such a 
kind as determines the intellect to most vigorous 
energy. The only profitable reading is that in which 
we are compelled to think, and think intensely ; 
whereas that reading which serves only to dissipate 
and divert our thought, is either positively hurtful, 
or useful only as an occasional relaxation from severe 
exertion. But the amount of vigorous thinking is 

a See Walton's Lives of Donne, fi Briefe iiber das Stud, der Theol. 

Wotto7i, Hooker, Herbert, and San- B. xlix., Werlce, xiv. 267, ed. 1829. 

derson, vol. ii. p. 287, ed. Zouch, — Ed. 
York, 1817.— Ed. 



First Rule. 



218 LECTUEES ON LOGIC. 

LECT. usually in the inverse ratio of multifarious readius;. 

XXXV • • • • 

'- Multifarious reading is agreeable; but, as a habit, it 

is, in its way, as destructive to the mental as dram- 
drinking is to the bodily health. 
IT. Quality II. In reference to the Quality of what is to be read, 
to be read, thc First of tho five rules is — ' Select the Avorks of prin- 
cipal importance, in accommodation either to the seve- 
ral sciences themselves, to your particular aim in read- 
ing, or to your individual disposition and wants.' This 
rule is too manifestly true to require any illustration 
of its truth. No one will deny that for the accom- 
plishment of an end, you ought to employ the means 
best calculated for its accomplishment. This is all 
that the rule inculcates. But while there is no diffi- 
culty about the expediency of obeying the rule, there 
is often considerable difficulty in obeying it. To know 
what books ought to be read in order to learn a science, 
is in fact frequently obtained only after the science has 
been already learned. On this point no general advice 
can be given. We have, on all of the sciences, works 
which profess to supply the advice which the student 
here requires. But in general, I must say, they are of 
small assistance in pointing out what books we should 
select, however useful they may be in showing us what 
books exist upon a science. In this respect, the British 
student also labours under peculiar disadvantages. 
The libraries in this country are, one and all of them, 
wretchedly imperfect ; and there are few departments 
of science, in which they are not destitute even of the 
works of primary necessity, — works which, from their 
high price, but more frequently from the difficulty 
of procuring them, are beyond the reach of ordinary 
readers. 

Under the head of Quality the Second Rule is — 



LECTURES ON LOGIC. 219 

' Read not the more detailed works upon a science, lect. 

until you have obtained a rudimentary knowledge oi 

it in general.' The expediency of this rule is suffi- Rule, 
ciently apparent. It is altogether impossible to read 
with advantage an extensive work on any branch of 
knowledge, if we are not previously aware of its general 
bearing, and of the relations in which its several parts 
stand to each other. In this case, the mind is over- 
powered and oppressed by the mass of details pre- 
sented to it, — details, the significance and subordina- 
tion of which it is as yet unable to recognise. A con- 
spectus,-^a survey of the science as a whole, ought, 
therefore, to precede the study of it in its parts ; we 
should be aware of its distribution, before we attend 
to what is distributed, — we should possess the empty 
frame-work, before we collect the materials with which 
it is to be filled. Hence the utility of an encyclo- 
paedical knQwledge of the sciences in general, prelimi- 
nary to a study of the several sciences in particular; 
that is, a summary knowledge of their objects, their 
extent, their connection with each other. By this 
means the student is enabled to steer his way on the 
wide ocean of science. By this means he always knows 
whereabouts he is, and becomes aware of the point 
towards which his author is leading him. 

In entering upon the study of such authors as Plato, 
Aristotle, Descartes, Spinoza, Leibnitz, Locke, Kant, 
&c., it is, therefore, proper that we first obtain a pre- 
paratory acquaintance with the scope, both of their 
philosophy in general, and of the particular work on 
which we are about to enter. In the case of writers 
of such ability this is not difiicult to do; as there are 
abundance of subsidiary works, affording the prelimi- 
nary knowledge of which we are in quest. But in the 



ii 



220 LECTURES ON LOGIC. 

LECT, case of treatises wliere similar assistance is not at band, 

XXXV 

1 '- we may often, in some degree, prepare ourselves for a 



regular perusal, by examining tbe table of contents, 
and taking a cursory inspection of its several depart- 
ments. In this respect and also in others, the follow- 
ing advice of Gibbon to young students is highly de- 

Gibbon serving of attention. " After a rapid glance (I trans- 
late from the original French) — after a rapid glance 
on the subject and distribution of a new book, I sus- 
pend the reading of it, which I only resume after hav- 
ing myself examined the subject in all its relations, 
— after having called up in my solitary walks all that 
I have read, thought, or learned, in regard to the sub- 
ject of the whole book, or of some chapter in particu- 
lar. I thus place myself in a condition to estimate 
what the author may add. to my general stock of know- 
ledge; and I am thus sometimes favourably disposed 
by the accordance, sometimes armed by the opposition, 
of our views."" 

Third Xhe Third Eule under the head of Quality is — 

Rule. '' 

' Make yourselves familiar Avith a science in its present 
state, before you proceed to study it in its chronologi- 
cal development.' The propriety of this procedure is 
likewise manifest. Unless we be acquainted with a 
science in its more advanced state, it is impossible to 
distinguish between what is more or less important, 
and, consequently, impossible to determine what is or 
is not worthy of attention in the doctrines of its earlier 
cultivators. We shall thus also be overwhelmed by, 
the infinitude of details successively presented to us ; 
all will be confusion and darkness, where all ought to 

a The substance of the above pas- pp. 54, f)5 ; ed. 1837. The French; 
sage is given in English, in Gibbon's original is quoted by Scheidler, Ho-, 
Memoirs of iny Life and Writings, degetik, § 55, p. 204. — Ed. 



LECTURES ON LOGIC. 221 

be order and light. It is thus improper to study lect. 
philosophy historically, or in its past progress, be- - — ^ — '- 



fore we have studied it statistically, or in its actual 
results. 

The Fourth Kule under the same head is — ' To Fourth 
avoid erroneous and exclusive views, read and com- 
pare together the more important works of every party.' 
In proportion as different opinions may be entertained 
in regard to the objects of a science, the more neces- 
sary is it that we should weigh with care and imparti- 
ality the reasons on which these different opinions rest. 
Such a science, in particular, is philosophy, and such 
sciences, in general, are those which proceed out of 
philosoph}^ In the philosophical sciences, we ought, 
therefore, to be especially on our guard against that 
partiality which considers only the arguments in favour 
of particular opinions. It is true that in the writings 
of one party we find adduced the reasons of the oppo- 
site party; but frequently so distorted, so mutilated, 
so enervated, that their refutation occasions little 
effort. We must, therefore, study the arguments on 
both sides, if we would avoid those one-sided and con- 
tracted views which are the result of party-spirit. 
The precept of the Apostle, " Test all things, hold fast 
by that which is good," is a precept which is applicable 
equally in philosophy as in theology, but a precept 
that has not been more frequently neglected in the 
one study than in the other. 

The Fifth Eule under the head of Quality is — ' To Fifth Rule, 
avoid a one-sided development of mind, combine with 
the study of works which cultivate the Understanding, 
the study of works which cultivate the Taste.' The 
propriety of this rule requires no elucidation. 

I therefore, pass on to the third head — viz. the 



222 LECTURES OX LOGIC. 

LECT. Manner of readine: itself: under which the First 

XXXV 

Rule is — ' Eead that you may accurately remem- 



of ReadrngT bcr, but stlll Hiorc that you may fully understand.' 
u e. rpi^-g ^|g^ requires no comment. Reading should not 
be a learning by rote, but an act of reflective think- 
ing. Memory is only a subsidiary faculty, — is valuable 
merely as supplying the materials on which the under- 
standing is to operate. We read, therefore, principally, 
not to remember facts but to understand relations. 
To commit, therefore, to memory what we read, before 
we elaborate it into an intellectual possession, is not 
only useless but detrimental ; for the habit of laying 
up in memory what has not been digested by the 
understanding, is at once the cause and the effect of 
mental weakness. 

Second The Second Rule under this head is — ' Strive to 

compass the general tenor of a work, before you at- 
tempt to judge of it in detail.' Nothing can be more 
absurd than the attempt to judge a part, before com- 
prehending the whole; but unfortunately nothing is 
more common, especially among professional critics, — 
reviewers. This proceeding is, however, as frequently 
the effect of wilful misrepresentation, as of uninten- 
tional error. 

Third Rule. The Third Rule under this head is — 'Accommodate 
the intensity of the reading to the importance of the 
work. Some books are, therefore, to be only dipped 
into ; others are to be run over rapidly ; and others 
to be studied long and sedulously.^ All books are not 
to be read with the same attention ; and, accordingly, ; 

Lectio cur- au ancicut distinction was taken of reading into lectio ! 

Lectio sta- cursoTia and lectio stataria. The former of these 
we have adopted m English, cursory readmg bemg ; 
a familiar and correct translation of lectio cursoria. i 



LECTURES ON LOGIC. 223 



Bat lectio stataria cannot be so well rendered by the lect. 
expression of stationary reading. " Eead not," says 



Bacon in his Fiftieth Essay — " read not to contradict q^Ted. 
and confute, nor to believe and take for granted, nor 
to find talk and discourse, but to weigh and consider. 
Some books are to be tasted, others are to be swallowed, 
and some few to be chewed and digested ; that is, 
some books are to be read only in parts ; others to be 
read, but not curiously ; and some few to be read 
wholly and with diligence and attention. Some books 
also may be read by deputy, and extracts made of 
them by others ; but that would be only in the less 
important arguments, and the meaner sort of books ; 
else distilled books are, like common distilled waters, 
fleshy things/' " One kind of books," says the great 
historian, Johann von Mtiller,'' "I read with great Johann von 
rapidity, for in these there is much dross to throw 
aside, and little gold to be found ; some, however, there 
are all gold and diamonds, and he who, for example, 
in Tacitus can read more than twenty pages in four 
hours, certainly does not understand him." 

Eapidity in reading depends, however, greatly on 
our acquaintance with the subject of discussion. At 
first, upon a science we can only read with profit few 
books, and laboriously. By degrees, however, our 
knowledge of the matters treated expands, the reason- 
ings appear more manifest, — we advance more easily, 
until at length w^e are able, without overlooking any- 
thing of importance, to read with a velocity which 
appears almost incredible for those who are only 
commencing the study. 

The Fourth Kule under this head is — ' Reo;ulate on Fourth 

° Rule. 

a Werhe, iv. 177. Cf. xvii. 253. 55, p. 204.— Ed. 
Quoted by Scheidler, Hodegetik, § 



224 LECTURES ON LOGIC. 

LECT. the same principle the extracts which you make from 

^ L the works you read.' 

So much for the Unilateral Communication of 
thought, as a mean of knowledge. We now proceed 
to the Mutual Communication of thought, — Confer- 
ence. 
Conference, This is either mere Conversation, — mere Dialoo;ue, 

—of two ' . ^ ,^ - 

kinds. or Formal Dispute, and at present we consider both 
of these exclusively, only as means of knowledge, — 
only as means for the communication of truth. 

1. Dialogue. The employment of Dialogue as such a mean, re- 

quires great skill and dexterity ; for presence of mind, 
confidence, tact, and pliability are necessary for this, 
and these are only obtained by exercise, independently 
of natural talent. This was the method which Socra- 
tes almost exclusively employed in the communication 
of knowledge ; and he called it his art of intellectuah 
midwifery, because in its application truth is not given 
over by the master to the disciple, but the master, by 
skilful questioning, only helps the disciple to deliver 
himself of the truth explicitly, which his mind had 
before held implicitly. This method is not, however, 
applicable to all kinds of knowledge, but only to those 
which the human intellect is able to evolve out of it- 
self, that is, only to the cognitions of Pure Keason. 

2. Disputa- Disputation is of two principal kinds, inasmuch as it 
and Writ- is Oral or written ; and in both cases, the controversy 

may be conducted either by the rules of strict logical 
disputation, or left to the freedom of debate. With- 
out entering on details, it may be sufficient to state, in 
Academical regard to Logical Disputation, that it is here essential 

disputation. , , . . i • j i 

that the point m question, — the status controversice, — 
the thesis, should, in the first place, be accurately de- 
termined, in order to prevent all logomachy, or mere 



LECTURES ON LOGIC. 225 

who denies the thesis, aud who is called the opponent, lect. 

may either call upon the disputant who affirms the '- 

thesis, and who is called the defendant, to allege an 
argument in its support, or he may at once himself 
produce his counter-argument. To avoid, however, all 
misunderstanding, the opponent should also advance 
an antithesis, that is, a proposition conflictive with the 
thesis, and when this has been denied by the defend- 
ant the process of argumentation commences. This 
proceeds in regular syllogisms, and is governed by 
definite rules, which are all so calculated that the dis- 
cussion is not allowed to wander from the point at 
issue, and each disputant is compelled, in reference to 
every syllogism of his adversary, either to admit, or 
to deny, or to distinguish." These rules you will find 
in most of the older systems of Logic ; in particular 
I may refer you to them as detailed in Heerebord's 
Praxis Logica, to be found at the end of his edition 
of the Synopsis of Burgersdicius. The practice of 
disputation was long and justly regarded as the most 
important of academical exercises ; though liable to 
abuse, the good which it certainly ensures greatly sur- 
passes the evil which it may accidentally occasion. 

a Cf. Krug, Lorjil; § 186. Aum. 2. Scheidler, Hodegetll; § 45, p. 138- Ed. 



VOL. IL 



APPENDIX. 



APPENDIX. 



I. 

THE CHARACTER AND COMPREHENSION OF LOGIC. 
—A FRAGMENT. 

(See above, Volume I., page 4.) 

In the commencement of a course of academical instruction, there 
are usually two primary questions wliich obtrude themselves ; 
and with the answer to these questions I propose to occupy the 
present Lecture. 

The first of these questions is, — AVhat is the character and 
comprehension of the subject to be taught ? The second, — What 
is the mode of teaching it ? In regard to the former of these, the 
question, — What is to be taught, — in the present instance is as- 
suredly not superfluous. The subject of our course is indeed pro- 
fessedly Logic ; but as under that rubric it has been too often the 
practice, in our Scottish Universities, to comprehend almost every 
thing except the science which that name properly denotes, it is 
evident that the mere intimation of a course of Lectures on Logic 
does not of itself definitely mark out what the professor is to 
teach, and what the student may rely on learning. 

I shall, therefore, proceed to give you a general notion of what 
Logic is, and of the relation in which it stands to the other 
sciences, for Logic, — Logic properly so called, — is the all-import- 
ant science in which it is at once my duty and my desire fully 
and faithfully to instruct you. 

The very general, — I may call it the very vague, — conception 
which I can at present attempt to shadow out of the scope and na- 
ture of Logic, is of course not intended to anticipate what is here- 
after to be articulately stated in regard to the peculiar character 
of this science. 



230 APPENDIX. 

All science, all knowledge, is divided into two great branches ; 
for it is either, 1°, Conversant about Objects Known, or, 2°, Con- 
versant about the Manner of knowing them, in other words, about 
the laws or conditions under which such objects are cognisable. 
The former of these is Direct Science, or Science simply; the 
latter, Keflex Science, — the Science of Science, or the Method of 
Science. 

Now of these categories or great branches of knowledge, Simple 
Science, or Science directly conversant about Objects, is again 
divided into two branches ; for it is either conversant about the 
phsenomena of the internal world, as revealed to us in conscious- 
ness, or about the phsenomena of the external world, as made 
known to us by sense. The former of these constitutes the 
Science of Mind, the latter the Science of Matter ; and each is 
again divided and subdivided into those numerous branches, which 
together make up nearly the whole cycle of human knowledge. 

The other category, — the Science of Science, or the Method- 
ology of Science, — falls likewise into two branches, according as the 
conditions which it considers are the laws which determine the 
possibility of the mind, or subject of science, knowing, or the 
laws which determine the possibility of the existence, or ob- 
ject of science, being known ; Science, I repeat, considered as 
reflected upon its own conditions, is twofold, for it either con- 
siders the laws under which the human mind can know, or the 
laws under which what is proposed by the human mind to know, 
can be known. Of these two sciences of science, the former, — 
that which treats of those conditions of knowledge which lie in 
the nature of thought itself, — is Logic, properly so called ; the 
latter, — that which treats of those conditions of knowledge which 
lie in the nature, not of thought itself, but of that which we 
think about, — this has as yet obtained no recognised appellation, 
no name by which it is universally and familiarly known. Vari- 
ous denominations have indeed been given to it in its several parts 
or in its special relations ; thus it has been called Heuretic, in so 
far as it expounds the rules of Invention or Discovery, Architec- 
tonic, in so far as it treats of the method of building up our ob- 
servations into system ; but hitherto it has obtained, as a whole, 
no adequate and distinctive title. The consequence, or perhaps 
the cause, of this want of a peculiar name to mark out the second 



APPENDIX. 231 

science of science, as distinguished from the first, is that the two 
have frequently been mixed up together, and that the name of 
Logic has been stretched so as to comprehend the confused assem- 
blage of their doctrines. Of these two sciences of the conditions 
of knowledge, — the one owes its systematic development prin- 
cipally to Aristotle, the other to Bacon ; though neither of 
these philosophers has precisely marked or rigidly observed the 
limits which separate them from each other ; and from the cir- 
cumstance, that the latter gave to his great Treatise the name of 
Organum, — the name which has in later times been applied to 
designate the complement of the Logical Treatises of the former 
— from this circumstance, I say, it has often been supposed, that 
the aim of Bacon was to build up a Logic of his own upon the 
ruins of the Aristotelic. Nothing, however, can be more errone- 
ous, either as to Bacon's views, or as to the relation in which the 
two sciences mutually stand. These are not only not mconsistent, 
they are in fact, as correlative, each necessary to, each dependent 
on, the other ; and although they constitute two several doctrines, 
which must be treated in the first instance each by and for itself, 
they are, however, in the last resort only two phases, — two mem- 
bers, of one great doctrine of method, which considers, in the 
counter relations of thought to the object, and of the object to 
thought, the universal conditions by which the possibility of hu- 
man knowledge is regulated and defined. 

But allowing the term Logic to be extended so as to denote the 
genus of which these opposite doctrines of Method are the species, 
it will, however, be necessary to add a difference by which these 
special Logics may be distinguished from each other, and from the 
generic science of which they are the constituents. The doctrine, 
therefore, which expounds the laws by which our scientific pro- 
cedure should be governed, in so far as these lie in the forms of 
thought, or in the conditions of the mind itself, which is the sub- 
ject in which knowledge inheres, — this science may be called For- 
mal, or Subjective, or Abstract, or Pure Logic. The science, again, 
which expounds the laws by which our scientific procedure should 
be governed, in so far as these lie in the contents, materials, or ob- 
jects, about which knowledge is conversant, — this science may be 
called Material, or Objective, or Concrete, or Applied Logic. 

Now it is Logic, taken in its most unexclusive acceptation 



S32 APPENDIX. 

which will constitute the object of our consideration in the follow- 
ing course. Of the two branches into which it falls, Formal Logic, 
or Logic Proper, demands the principal share of our attention, and 
this for various reasons. In the first place, considered in reference 
to the quantity of their contents. Formal Logic is a far more com- 
prehensive and complex science than Material. For, to speak first 
of the latter : — if we abstract from the specialities of particular 
objects and sciences, and consider only the rules which ought to 
govern our procedure in reference to the object-matter of the sci- 
ences in general, — and this is all that a universal Logic can pro- 
pose, — these rules are few in number, and their applications simple 
and evident. A Material or Objective Logic, except in special 
subordination to the circumstances of particular sciences, is, there- 
fore, of very narrow limits, and all that it can tell us is soon told_ 
Of the former, on the other hand, the reverse is true. For though 
the highest laws of thought be few in number, and though Logic 
pro2:)er be only an articulate exposition of the universal necessity 
of these, still the steps through which this exposition must be ac- 
complished, are both many and multiform. 

In the second place, the doctrines of Material Logic are not 
only far fewer and simpler than those of Formal Logic, they are 
also less independent ; for the principles of the latter, once estab- 
lished, those of the other are either implicitly confirmed, or the 
foundation laid on which they can be easily rested. 

In the third place, the study of Formal Logic is a more improv- 
ing exercise ; for, as exclusively conversant with the laws of thought, 
it necessitates a turning back of the intellect upon itself, which is 
a less easy, and, therefore, a more invigorating, energy, than the 
mere contemplation of the objects directly presented to our observa- 
tion. 

In the fourth place, the doctrines of Formal Logic are possessed 
of an intrinsic and necessary evidence, they shine out by their 
native light, and do not require any proof or corroboration beyond 
that which consciousness itself supplies. They do not, therefore, 
require, as a preliminary condition, any apparatus of acquired 
knowledge. Formal Logic is, therefore, better fitted than Material, 
for the pm-poses of academical instruction ; for the latter, primarily 
conversant with the conditions of the external world, is in itself a 
less invigorating exercise, as determining the mind to a feebler and 



APPENDIX. 233 

more ordinary exertion, and, at the same time, cannot adequately 
be understood without the previous possession of such a comple- 
ment of information, as it would be unreasonable to count upon in 
the case of those who are only commencing their philosophical 
studies. 



II. 

GENUS OF LOGIC. 

(See above, Vol. I., p. 9.) 

I. — SCIENCE. 
A. Affirmative. 

Stoici, (v. Alexander Aphrod. In Topica, Prooem. ; Diogenes 
Laertius, Vita Zenonis, L. vii., § 42). "Plato et Platonici et 
Academici omnes," (v. Camerarius, Selectee Dispiit Philos. Pars. 
i., qu. 3, p. 30). 

(«)— SPECULATIVE SCIENCE. 

Toletus, In Un. Arist. Log., De Dial, in Communi, Qu. ii., iv. 
Suarez, Disp. Metaph.., Disp. i. § iv. 26 ; Disp. xliv. § xiii. o-i. 
"Communiter Thomistse, ut Capreolus, Sotus, Masius, Flandra, 
Soncinas, Javellus : Omnes fere Scotistse cum Scoto, ut Valera, 
Antonius Andreas, &c." (v. Ildephonsus de Penafiel, Logicce Dis- 
putationes, Disp. i. qu. 4. Cursus, p. 79.) For Aquinas, Dm-andus, 
Niphus, Canariensis, see Antonius Ruvio, Co7n. in Arist. Dialect, 
Prooem. qu. 5. For Bacchonus, Javellus, Averroes, see Conimbri- 
censes, In Arist. Dial. Prooem. Q. iv. art. 5. Lalemandet, Cur- 
sus PJiil, Logica, Disp. iii. part iii. Derodon, Logica Restit., De 
Genere, p. 4.5. Camerarius, Disp. Phil., Pars i., qu. 3, 4. (That Lo- 
gica docens a true science). For Pseudo-Augustinus, Avicenna, 
Alpharabius, see Conimbricenses, Com. in Arist. Dial. Prooem. Qu. 
iv. art. 3. For Boethius, Mercado, Vera Cruce, Montanesius, see 
Masius, Co7n. in Porpli. et in Universam Aristotelis Logicanij 
Sect, i., Prooem. qu. v. et seq. Poncius, De Nat. Log., Disp. ii., 
concl. 2. For Rapinseus, Petronius, Faber, see Camerarius, Sel. 
Disp. Phil, Pars i., qu. 4, p. 44. 



234 APPENDIX. 



(6) — PRACTICAL SCIENCE. 

Conimbricenses, In Univei'sam Aristotelis Dialecticam 
Prooem. Qu. iv., art 5. Fonseca, In Iletaph. L. ii. c. 3, qu. 
1, § 7. For Venetus, Albertus Magnus, Jandunus, see Ruvio, 
I. c. Schiller, Philosophia nova Methodo Explicata. Pars Prior, 
L. V. ex. i., p. 306. (1603). D'Abra de Raconis, Summa Totius 
Philosophice, Log. Prcel, c. i. Isendoorn, Cursiis Logicus, L. 
i., c. 2, qu. 7. Biel, In Sentent., L. ii. Prol. Occam, Summa 
Totius Logicce, D. xxxix. qu. 6. For Aureolus, Bern. Mirandulanus 
see Conimbricenses, I. c. For Mathisius, Murcia, Vasquez, Eckius, 
see Camerarius, Sel. Disp. Phil. Pars, i., qu. 4, p. 44. Ildephon- 
sus de Penafiel, Log. Disp. D. i. qu. 4, sect. 2. Oviedo, Cursus 
Philosophicus, Log., Contr. Prooem. ii. 5. Arriaga, Cursus Philo- 
sophicus, Disp. iii. § 4. 



(c) — SPECULATIVE AND PRACTICAL. 

Hurtado de Mendoza, Log. Disp. D. ii. § 2. 

B. Negative. 

For almost all the Greek commentators, see Zabarella, Opera 
Logica, De Nat. Log., L. i. c. 5, and Smiglecius, Logica, D. ii. qu. 5. 
See also Ildephonsus de Penafiel, Disp. Log. D. i. qu. 1, § 1, p. 67. 

II. — ART. 

Scheibler, Opera Logica, Pars, i, c. 1, p. 49. J. C. Scaliger, 
Exercitationes, Exerc. i. 3. G. J. Vossius, De Natura Artium, 
L. iv., c. 2, § 4. Balforeus, In Org. Q. v. § 6, Prooem., p. 31. 
Burgersdicius, Institutiones Logicce. Lib. i. c. 1. Pacius, Comm. 
in Org. p. 1. Sanderson, Log. Artis Compendium, L. i. c. 1, p. 1, 
Cf. p. 192. Aldrich, Artis Log. Compendium. L. i. c. 1, p. 1. 
Hildenius, Qumstiones et Commentaria in Organon, p. 579 (1585.) 
Goclenius, Prohlemata Logica et Philosophica. Pars. i. qu. 3. 
Ramus, Dialectica. L. i. c. 1. Augustinus, De Ordine, ii. c. 15. 
Cicero, De Claris Oratoribus, c. 41. De Oratore, L. ii., c. 38. 



APPENDIX. 235 

Lovanienses, Com. in Arist. Dial. Prsef. p. 3. Rodolphus Agricola, 
De DialecticcB Inventione, L. ii. p. 255. Monlorius, (Bapt.), 
Comm. in Anal. Pr. PrsBf. Nunnesius, De Constitut. Dial., p. 43. 
Downam, (Ramist), Comm. in Ram. Dial., L. i. c. 1 , p. 3. Paraeus, 
Ars Logica, p. 1, 1670. Por Horatius Coruachinus, Ant. Bernardus 
Mirandulanus, Plamminius Nobilius, see Camerarius, Sel. Disp. 
Phil Pars. i. q. 3, p. 30. 



III.— SCIENCE AND ART. 

Lalemandet, Log., Disp. iii. Part iii. cl, 4. (Logica utens, an 
art ; Logica docens, a speculative science.) Tartaretus, In P. 
Hispanum, f. 2, (Practical Science and Art.) P. Hispanus, Copu- 
lata Omn. Ti^actat. Pet. Hisp. Parv. Logical. T. i. f. 10, 1490. 
Philosophia Vetus et Kova in Regia Burgundia dim Pertractata, 
Logica, T. I., pp. 58, 59. 4tli ed. London, 1685. Tosca, Comp. 
Phil. Log., Tr. i. 1. iv. c. 4, p. 208, (Practical Science and Art). 
Purchot, Instil. Phil., T. I. Prooem. p. 36. Eiigenius, AoytK-r), pp. 
140, 141. Dupleix, Zo^igwe, p. 37. ^SiCciol^iii, RudimentaLogicce, 
p. 5. Schmier, Philosophia Quadripartita, (v. Heum annus, j4cto 
Philosoph., iii. p. 67.) Aquinas (in Caramuel, Phil. Realis et 
Rationalis, Disp. ii. p. 8). 

IV. — NEITHER SCIENCE NOR ART, BUT INSTRUMENT, ORGAN, OR 
HABIT, OR INSTRUMENTAL DISCIPLINE. 

Pliiloponus, In An. Prior., initio. For Animonius, {Prcef. in 
Prced.), Alexander, (In Topica, i. c. 4 ; Metaph. ii. t. 15). 
Simplicius, (Prcef. in Priced.), Zabarella, {De Notura Logicce, L. 
i. c. 10.), Zimara, (In Tabida v. Ahsurdum^, Averroes, see 
Smiglecius, Logica, Disp, ii. qu. 6, p. 89. Aegidius, In An. Post. 
L. i. qu. 1. For Magnesius, Niger (Petrus), Villalpandeus, see 
Ruvio, In Arist. Dial., prooem. qu. 2. F. Crellius, Isagoge Lo- 
gica, L. i. c. 1. p. 5. P. Vallius, Logica, T. I. prooem. c. i. et alibi. 
Bartholinus, Janitores Logici, II. pp. 25 and 76. Bertius, Logica 
Peripatetica, pp. 6, 10. Themistius, An. Post. i. c. 24. Aquinas, 
Opuscula, 70, qu. De Divisione Scientim Specidativce, — sed alibi 
scientiam vocat. (See Conimbricenses, I71 Arist. Dial., T. I. qu. 



236 APPENDIX. 

iv. art. 5, p. 42). Balduimis, In Qiicesito an Logica sit Scientia. 
Scaynus, Paraphrasis in Org anon. Prsef. p. 9. 



V. — THAT, LOOSELY TAKING THE TERMS, LOGIC IS EITHER ART, 
OR SCIENCE, OR BOTH. 

Zabarella, Opera Logica, De Nat. Log., L. i. c. viii. D'Abra 
de Eaconis, Summa Tot. Phil. Prcel. Log., L. iii., c. 1, p. 8, ed. 
Colon., (Practical Science), Balforeus, In Organon, Q. v. §§ 1, 6, 
pp. 20, 32. (Art). Derodon, Logica Restit. De Prooem. Log., 
p. 49, (Speculative Science). Crellius, Isagoge, pp. 1, 4. Bertius, 
Logica Peripatetica, pp. 11, 13. Aldrich, Art. Log. Comp., L. ii. 
c. 8, T. i. (Art). Sanderson, Log. Art. Comp. Append. Pr., c. 2, 
p. ] 92. (Art). Conimbricenses, InArist. Dial., T. I., p. 33. (Practi- 
cal Science). Philosophia Burgundia, T. I. pp. 56, 59. Eustachius, 
Summa Philosophia', Dialectica, Qucest. Prooem., i. p. 4. Nim- 
nesius, De Constit. Dial., ff. 43, 68. Scheibler, Opera Logica, 
pp. 48, 49. Scaynus, Par. in Org., pp. 11, 12. Camerarius, Sel. 
Disp. Phil., Pars. i. qu. 3, pp. 81, 38 (Speculative Science). B. 
Pereira, De Commun. Princip. Omn. Per. Katural., L. i. De Phil. 
c. 18, p. 60, 1618. 



VI. — THAT AT ONCE SCIENCE (PART OF PHILOSOPHY) AND 
INSTRUMENT OF PHILOSOPHY. 

BoetMus, Prcef. in Porphyr. (a Victorino Transl.) Opera, p. 48. 
Eustachius, Summa Philosopliice, p. 8, (Scientia organica et prac- 
tica.) For Simplicius, Alexander, Philoponus, &c., see Camerarius, 
Sel. Disp. Phil., p. 30. Pacius, Com. in Arist. Org., p. 4. 



VII. — THAT QUESTION, WHETHER LOGIC PART OF PHILOSOPHY 
OR NOT, AN IDLE QUESTION. 

Pacius, Com. in A7'ist. Org., p. 4. Avicenna, (in Conimbri- 
censes, In Arist. Dial, Qu. iv. art. 4, T. I. p. 38.) 



APPENDIX. 237 



Vlll. — THAT QUESTION OF WHETHER ART, SCIENCE, &C., IDLE 
— ONLY VERBAL. 

Buffier, Gours des Sciences^ Seconde Logique, § 421, p. 887. 
Eugenius, 'H AoytKi), p. 140, has the following : — 
" Prom what has been said, therefore, it clearly appears of what 
character are the diversities of Logic, and what its nature. For 
one logic is Natural, another Acquired. And of the Natural, 
there is one sort according to Faculty, another according to Dis- 
position. And of the Acquired, there is again a kind according to 
Art, and a kind according to Science. And the Native Logic, 
according to Faculty, is the rational faculty itself with which every 
human ^individual is endowed, through which all are qualified for 
the knowledge and discrimination of truth, and which, in propor- 
tion as a man employs the less, the less is he removed from irra- 
tionality. But the Native Logic, according to Disposition, is the 
same faculty by which some, when they reason, are wont to exert 
their cogitations with care and attention, confusedly, indeed, and 
uncritically, still, however, in pursuit of the truth. The Acquired, 
according to Art, is the correct and corrected knowledge of the 
Ptules, through which the intellectual energies are, without fault 
or failure, accomplished. But the Acquired, according to Science, 
is the exact and perfect knowledge both of the energies themselves, 
and also of the causes through which, and through which exclu- 
sively, they are capable of being directed towards the truth." 

[ Native, according to j j^-'posftion. 

Logic. < 

f Acquired, according to < rj • ' 
^ ^ ' ( Science. 

" And thus Disposition adds to Faculty consuetude and a 
promptness to energise. Art, again, adds to Disposition a refine- 
ment and accuracy of Energy. Finally, Science adds to Art the 
consciousness of cause, and the power of rendering a reason in the 



238 APPENDIX. 

case of all the Rules. And the natural logician may be able, in his 
random reason, to apprehend that, so to speak, one thing has de- 
termined another, although the nature of this determination may 
be beyond his ken. But he whose disposition is exercised by re- 
flection and imitation, being able easily to connect thought with 
thought, is cognisant of the several steps of the reasoning process, 
howbeit this otherwise may be confused and disjointed. But he 
who is discipKned in the art, knows exactly that, in an act of infer- 
ence, there are required three terms, and that these also should be 
thus or thus connected. Finally, the scientific logician under- 
stands the reason, — why three terms enter into every syllogism, — 
why there are neither more nor fewer, — and why they behove to 
be combined in this, and in no other fashion. 

" Wherefore to us the inquiry appears ridiculous, which is fre- 
quently, even to nausea, clamorously agitated concerning Logic — 
Whether it should be regarded as an Art or as a Science." 



APPENDIX. 



239 



III. 

DIVISIONS, VAEIETIES, AND CONTENTS OF 
LOGIC. 

(See above, Vol. I., p. 68.) 



1. LOGICA, < 



Docens, 
X^piy ■KpayiJ.a.Twv, 

Utens, 
iv xp'^'^^^ '"*^ yv/xvacria 
■Kpa.yfx.aTwv, 



f\. Timpler, Logicce Systema, L. i. c. 
i. qusest. 2, 3. Isendoom, Effata, 
Centuria, i. Eff. 55. Crellius, 
Isagoge, Pars Prior, L. i. c. i. p. 12. 
Noldius, Logica Recognita, Prooem. 
p. 13. 
Philoponus, In. An. Pr., f. 4. Al- 
steclius, Encyclopcedia, pp. 29 and 
406. V. Aristotle, Aletaph., L. vii. 
text, 23. 



II. Logica, 



Doctrinalis ) [Objec- 
Systematica ) tiva], 
Habitualis,[Subjectiva], 



V. Timpler, Syst. Log., Appendix, p. 
877. Noldius, Log. Recog., Prooem., 
p. 13. 



III. Logica, , 



Pars Communis, Gene 

ralis, ^ 

Pars Propria, Specialis, 



adopted in dififerent significations by 
Timpler, Syst. Log., q. 19, p. 55. 
Theoph. Gale, Logica, pp. 6, 246, 
et seq. (1681.) Crellius, Isagoge, P. 
i. L. i. c. 1, p. 3. Alstedius, Eticy- 
clop., pp. 29 and 406. 



IV. Logica, 



Pura, 
Applicata, 



N.B. — Averroes, (Pacins, Com. p.2), 
has Logica ajipropriata sen particida- 
ris, and Logica communis =Universal, 
Abstract Logic. 



V. Logica, 



Abstracta, 
Concreta. 



Pars Commimis, 



VI Logica/ { Apodictica, v. Timpler, .S'i/s^. io^r., p. 42. Iseu- 

• ^««^*-^'^ P^r^Pro- U.^1^^^.^^^ I doom, Efafa, Cent. i. Eff. 56. 

P"^' ( Sophistica, 



240 



APPENDIX. 



EiipeTLKTI Vel TOTTIKT], 

Inventio. 



VII. LocaCA, ( KpiriKTi. 
Jiuliciiiin. 
Dispositio. 



^v. Timpler, Syd.Log.,-^. 44. Crellius, 
Isagoge, pp. 10, 11, and Isendoorn, 
Effata, Cent. i. Eff., 51. Adopted 
by Agricola, De Inv. Dial., L. i. 
p. .35. MelancMiou, Erot. Died., 

J p. 10. Ramus, Schol. Dialect., L. 
i. c. i., and L. ii. c. i. p. 351 et 
seq. Sjieucer, Log., p. 11. Dow- 
n.im, In Rami Dial., L. i. c. 2, p. 
14. Perioniiis, De Dialedica, L. i. 
J). 6, (1544). Vossius, i)e iV^ai. Arti- 

^ um dive Logica, L. iv. c. ix. p. 217. 



VIII. Logica, 



Pars de Propositio. 
Pars de Judicio. 



V. Timpler, Sysf. Log., j). 49. 



I Doetrina Dividend! . j v. Timpler, S>/st. Log. p. 51. Isen- 

IX. Logica, < Doctriua Definiendi. > doom, Effata, Cent. i. Eff., 57. 

/ Doetrina Argiimentaudi. \ Boethius, (Aiigustin, Fonseca, &c.) 



X. Logica,* 



Sunplicis Apprehensi- 

onis. 
Judicii. 
Eatiocinationis. 

Noijtica, {melius Noema- 
Synthetica. tica.) 

Diauoetica. 



^ 



V. Timpler, Syst. Log., 52. Isen- 
doorn, Effata, Cent. i. Eff., 58. 
\ Isendoorn, Cursus Logicus, p. 31, and 
Effata, Cent. i. § 59. Noldius, Log. 
Hec, p. 9. Aquinas. 



J 



XI. Logica, 



1. Ideas (notions). 

2. Judgment. 

3. Peasoning. 

4. Method. 



UAH de Pemer, Part i. Clericus, 
Logica, adopts this division, but 
makes Method third. Reasoning 
fourth. 



XII. Logica, 



1. Doctrine of Elements. 

2. Doctrine of Method. 



Kant, Logik ; Krug, Logik. 



1st, Called Analytic by Metz, Inst it. Log. Twesten, Die Logik, 
inshesondere die Analytik, p. hi. Esser, Logik. Part i. 

2d, Called Systematic or Architectonic by Bachmami, Logik, 
Part ii. 

Called Synthetic by Esser (who includes xmder it also Applied 
Logic), Logik, Part ii. 



APPENDIX. 



241 



XIII. LOGIC-E 



IThematica — de materia 
operatioui Logicse 
siibjecta. 
Organica — ■ de iustru- 
mentis sciendi. 



Mark Dimcan, Instittdiones Logicce, 
Proleg. c. iii. § 2, p. 22. Bvirgersdi- 
chis, Instit. Log.^ L. i. c. i. p. 5. 



/'I. De ordiuibus rerum generalibus 
et attribiitis communissimis. 
2. De Vocibiis et Oratione. 
Commimis ^- ^^ Ideis simplicibus et appre- 
Generalis \ bensione simplici dirigenda, 

4. De Jiidicio et Propositione. 

5. De Discursii. 

6. De Dispositione seii Methodo. 



XIV. LoGiCA, ( Specialis, 



Genetica. 



I Genesis stricta. 
C Genesis didactica. 



(Genesis 
sen 
Inventio 

( Hermenentica. 
Analysis | ^nalytica and Critica. 

In ordine ad meutem — Logica 

stricte dicta. 
In ordine ad alios — Interpretativa 

vel Hemieueiitica genetica. 



I Hermenentica aualytica. 
Analytica stricta vel in specie. 



Tbeophilus 
Gale (Logica, 
1681), foUows, 
(besides Kec- 
kermann and 
Bnrgersdyk), 
principally 
Clauberg and 
VArt de Pen- 
ser of Port 
Royal. 



XV. LoGiCxV, 



Theoretica pars. ^ 

Practica pars— (this in- 1 -yyoif^ PMlos. Rationalis, Pars 
eluding the Method- / ^^^^ jj_ 
ology and Applied 
Logic of Kant.) j 



XVI. 



On Adrastean order, &c. of the books of the Organon, vide 
Ramus, Scliolce Dial, L ii., c. 8., p. 354. Piccartus, In 
' Orgaimm, Prolegomena, p. 1 et seq. 



n. riepi T7)9 TrpaJTTjs ivvoias, or 



irpoAiitfecos. 
XVI.* Logics 1 2. Xlepi (TKi^eus. 
partes, \3. nepl /cpitrews. 
4. Xlepi ^lavoias. 
I 5. Ilepl fi.iQ6Zov. 



Eugenins Diaconus, Aoyin)}, 
p. 144. 



VOL. II. 



242 



APPENDIX. 



XVII. LOGICA, 



1. Emendatrice. 

2. Inventrice. 

3. Giudicatrice. 

4. Ragionatrice. 

5. Ordinatrice. 



Genovesi. A division different in some 
respects is given in his Latin Logic, 
Proleg. § 51, p. 22. The fourth 
l)art of the division in the Latin 
Logic is omitted in the Italian, 
or rather reduced to the second, 
and the fifth divided into two. 



XV^III. LoGICA, 



Vetus, 



Nova, 



Por2)7iyrii Isag. 
Praed. . . 
Inter^wet. 

Anahjt. Pr. 
Analyt. Post 
Top. . . 
Elench. . . 



Isendoorn, Effafa, Cent. i. Eff. 
52. 

Eeason of terms, Pacius, Com- 
ment. in Org., In Porph. Isag. 
p. 3. 



"XroxewAoyiKri. , 

1 Isendoora, Effata, Cent. i. 

XIX. LoGiCA, I ( Apodictica. I Eff. 56. (From John Hos- 

•S,v\\oyL(TTiKi). J Topica. pinian, De Controversiis 

( Sophistica. Dialedicis.) 



XX. LOGICA, 



SroixeioAoyiKi';. 



Analytica 



( Prior. 

ca J 



Posterior. 



I Vossius, De Natura 
Artium sive de Lo- 
tuWoyiffTiK-i). 1 r • I (/i'^'^f L. iv. C. ix. p. 

Dialectica J Topica. I 220. 
Sophistica. 



XXI. LOGICA, 



( prodromus de Interj^retatione. 
-Analytica I universe de Syllogism o. 

(. speciatim de Demoustratione. 



XXII. LoGICA, 



ijirodromus de Categoriis. 
de Syll. verisimili. 
de Syll. sophistico sive pirastico. 



Vossiiis, De 
) Natura Ar- 
tium, p. 220. 



\ Dialectica. 



^ Analytica. 



Aristotle, in Laertius v. Vossius, De 
Nat. Art. siveDe Logica, L. iv. c. ix. 
§ 11, p. 219. 



XXIII. Logica j Rebus quae significantur.l 
de \ Vocibus quae significant.] 



Stoicorum, see Vossius, De Nat. Art. 
sire De Logica, L. iv. c. ix. § 7, 
p. 218. 



Loquendo. 
XXIV. LoGia?i I Eloquendo. (^Varro, vide Vossius, De. Nat. Art., 

partes de ] Proloquendo. / L. iv. c. ix. § 8, p. 219. 

Proloquiorum summa. 



APPENDIX. 



243 



XXV. LOGICA, 



Logica, 



Logicse 
partes, 

Logicse 
partes, 



nphs eiipecTiv. 
Tlphs Kpiaiv. 
Tlphs xpVC"^- 

NorjTi/cr;, Apprehensiva. 
KpLcri/jLos vel KpiTiK-ij, 

Judicativa. 
AiaXfKTtK-f], Argiunenta- 

tiva. 



Divisio. 

Defiiiitio. 

Argiunentatio. 

SApodictica. 
Dialectica. 
Sophistica. 



Logicse ( Analytica. 
partes, ( Tojiica. 



Aristotle (?) in Laertius, L. v. 
§ 28, p. 284. Alexander Aplirod. 
in nota Aldobrandini. 

Caramiiel Lobkowitz, Eationalis 
et Realis PhilosopMa, Logica 
sen Phil. Bat. Disp. ii. p. 3. 



V. Crellius, Isagoge, Pars, prior, c. i. p. 10. 



V. Crellius, Isagoge, Pars, prior, c. i. p. 10. 
Isendoorn, Effata, Cent. i. Eff. 54. 

> Crellius, Isagoge, Pars, prior, c. i. p. 10. 



Stoiclieiology (pure) should contain the doctrine of Syllogism, 
without distinction of Deduction or Induction. Deduction, Induc- 
tion, Definition, Division, from the laws of thought, should come 
under pure Methodology. All are processes, (v. Ceesalpinus, 
Qiuest. Perip. sub init.) 

Perhaps, 1°, Formal Logic, (from the laws of thought proper), 
should be distinguished from, 2°, Abstract Logic, (material, but of 
abstract general matter) ; and then, 3°, A Psychological Logic might 
be added as a third part, considering how Reasoning, &c., is affected 
by the constitution of om^ minds. Applied Logic is properly the 
several sciences. 

Or may not Induction and Deduction come mider abstract 
Material Logic? 



244 APPENDIX. 

IV. 
LAWS OF THOUGHT. 

(See Vol. I, p. 84.) 




C is either r or uon r 

The laws of Identity and Contradiction, each infers the other, 
but only through the principle of Excluded Middle ; and the prin- 
ciple of Excluded Middle only exists through the supposition of 
the two others. Thus, the principles of Identity and Contradiction 
cannot move, — cannot be applied, except through supposing the 
principle of Excluded Middle ; and this last cannot be conceived, 
existent, except through the supposition of the two former. They 
are thus co-ordinate but inseparable. Begin with any one, the 
other two follow as corollaries. 



(a) — Peimary Laws of Thought,— in geneeal. 

See the following authors on : — Dreier, Disput. ad Philoso- 
phiam Frimam, Disp. v. Aristotle, Analyt. Post. i. c. 11, §§ 2, 
3, 4, 5, 6, 7. Schramm, Philosophia Aristotelica, p. 36. Lippius, 
Metapyhsica Magna, L. i. c. i., p. 71 et seq. Stahl, Reguloi Philo- 
sophicoi, Tit. i., reg. i. p. 2 et seq., reg. ii., p. 8 et seq.. Tit. xix. 
reg. viii., p. 520 et seq. Chauvin, Lexicon Philosophicum, v. 
Metaphysica. Bisterfeld, evolves all out of ens, — ens est. See 
Philosophia Prima, c. ii. p. 24 et seq. Bobrik, System der Logik, 
§ 70, p. 247 et seq. 

Laws of Thought are of two kinds : — 1°. The laws of the Think- 
able, — Identity, Contradiction, &c. 2°. The laws of Thinking in 



APPENDIX. 245 

a strict sense — viz. laws of ConceptioB, Judgment, and Eeasoning. 
See Sclieidler, Psychologie, p. 15, ed. 1833. 

That they belong to Logic : — Ramus ScJiol. Dial., L. ix, p. 549. 

Is Affirmation or Negation prior in order of thought ? and thus 
on order and mutual relation of the Laws among themselves, as 
co-ordinate or derived ; (see separate Laws). Fracastorius, Opera, 
De Intellectione, L. i. f. 1 25 b., makes negation an act prior to 
affirmation ; therefore principle of Contradiction prior to principle 
of Identity. — Esser, LogiJc, § 28, p. 57. Sigwart, Handbuch su 
Vorlesungen uher die Logik, § 38 et seq. Piccolomineus, Le 
Mente Humana, L. iii., c. 4. p. 1301, on question — Is affirmative or 
negative prior ? Schulz, Prilf. der Kant. Krit. der reinen Vernunft, 

1. p. 78., 2d ed. Weiss, Lehrhuch der Logik, § 81 et seq. pp. 
61, 62, 1805. Castillon, Memoires de VAcademie de Berlin 
(1803) p. 8, (ContratUction and Identity co-ordinate). A. Andreas, 
In Arist. Metaph. iv. Qu. 5, p. 21. (Affirmative prior to nega- 
tive.) Leibnitz, CEuvres Philosophiques, Nouv. Ussais, L. iv. ch. 

2, § 1, p. 327, ed. Easpe. (Identity prior to Contradiction.) Wolf, 
Ontologia, §§55,288 — (Contradiction first. Identity second). Dero- 
don, Metaphysica, c. iii., p. 75 et seq. 1669. (Contradiction first. 
Excluded Middle second. Identity third). Eonseca, In Metaph., 
I. 849. Biunde, Psychologie, Vol. I, part ii. § 151, p. 159. (That 
principle of Contradiction, and principle of Reason and Consequent 
not identical, as Wolf and Reimarus hold.) Nic. Taurellus, Philo- 
sophic Triumphus, &c., p. 124. Arnheim, 1617. "Cum simplex 
ahqua sit affinnatio, negatio non item, banc illam sequi concludi- 
mus,'' &c. Chauvin, Lexicon Philosophicum, v. Metaphysica. 

By whom introduced into Logic : — Eberstein, {Uher die Bes- 
chaffenheit der Logik und Metaphysik der reinen Peripatetiker, 
p. 21, Halle, 1800), says that Darjes, in 1737, was the first to in- 
troduce Principle of Contradiction into Logic. That Buffier, and 
not Reimarus, first introduced principle of Identity into Logic, 
see Bobrik, Logik, § 70, p. 249. 

(b) — Peimaey Laws of Thought, — in particular. 
1. Principle of Identity. " Omne ens est ens." Held good by An- 



246 APPENDIX. 

tonius Andreas, In Metaph. iv., qu. 5. (apud Fonsecam, In Metaph. 
I. p. 849 ; melius apud Suarez, Select. Disp. Metaph. Disp. iii. 
sect. iii. n. 4.) Derodon, Metaphysica, c. iii., p. 77. J. Sergeant, 
Method to Science, p. 133 — 136 and after. (Splits it absurdly.) 
Boethius — " Nulla propositio est verier ilia in qua idem prpedicatur 
de seipso." (Versor, In P. Hispani Summulas Logicales, Tr. 
vii., p. 441 (1st ed. 1487); et Bmidnnus, Li Sophism.) " Pro- 
positiones illas oportet esse notissimas per se in quibus idem de se 
ipso prsedicatur, ut ' Homo est homo,' vel quarum prsedicata in 
definitionibus subjectarum includuntur, ut 'Homo est animal.'" 
Aquinas, Contra Gentiles, L. i. c. 1 0. Opera T. XVIII. p. 7, Venet. 
1786. Prior to principle of Contradiction — Leibnitz, Nouveanx 
JEssais, p. 377. Buffier, Principes du Raisonnement, 11. art 21, p. 
204. Rejected as identical and nugatory by Fonseca, loc. cit. 
Suarez, loc. cit. Wolf, Ontologia, §§ ob, 288, calls it Principium 
Certitudiuis, and derives it from Principium Contradictionis. 

2. Principle of Contradiction — a^tw/xa rrjs az/Tt^acreo)?. 

Aristotle, Metaph., L. iii. 3 ; x. 5. (Fonseca, In Metaph. T. I., p. 
850, L. iv. (iii.) c. 3.) Anal. Post. L. i. c. 11 c. 2, § 13. (On Aidstotle 
and Plato, see Hansel's Prolegomena, pp. 283, 284.) Stahl, Rs- 
gulce Philosophicce, Tit. i. reg. i. Suarez, Select Disp. Phil., Disp. 
iii. § 8. Timpler, Metaph. L. i., c, 8 qu. 14. Derodon, Meta- 
physica, p. 75 etc. Lippius, Metaphysica, L. i. c. i., p. 73. Ber- 
nardi, Thes. Aristot., vv. Principium, Cont7^adictio. Leibnitz, 
Oeuvres Philosophiques, Nouv. Ess., L. iv. c. 2. Ramus, "Axioma 
Contradictionis," Scholce Dial. L. ix. c. i., L. iv. c. 2, § 1, p. 548. 
Gul. Xy lander, Institutiones Aphoristicce Logices Aristot, p. 24, 
(1577), "Principium principiorum, hoc est, lex Contradictionis." 
Philoponus, d^Lcoixa rrjs dvTL(f)da€co<;, v. In Post. An. f. 30 b. et 
seq. Ammonius, d^tw/xa Trj<5 dpTL(f)dcre(o<5, In Dc Interpret, f 
94, Aid. 1503 ; but principium Exclusi Medii, Scheibler, Topica, c. 
19. On Definition of Contradictories, v. Scheibler, Ihid. On Two 
Principles of Contradiction, — Negative and Positive, v. Zabarella, 
Opera Logica, In An. Post. i. t. 83, p. 807. 

Conditions of — Aristotle, Metaph., L. iv., c. 6. Bemardi, The- 
saurus Arist., v. Contrad., p. 300. 

Proof attempted by — Clauberg, Ontosophia, § 26, (Degerando, 
Histoire de Philosophie, T. II. p. 57), through Excluded Middle. 



APPENDIX. 247 

3. Principle of Excluded Middle — d^toj/xa Stat/oert/coV. 

Agicofxa OLaiperiKov, divisivum, dicitur a Grsecis prmci^WM^i 
contradictionis afirmativum ; ' Oportet de omni re affirmare aiit 
negare,"' Goclenius, Lea^'icon Philosophicum. Lat. p. 136. Zaba- 
rella, In. An. Post., L. i., text 83, 02}era Logica, p. 807. Con- 
imbricenses, I)i Org., II., 125. Lucian, Opera, II. p. -l-i, (ed. 
Hemsterhuis). Aristotle, Metaph., L. iv. (iii.) c. 7 ; An. Post, L. i. 
2 ; ii. 13, (Maiisel's Prolegomena, p. 283). Joannes Pliiloponus, 
(v. Bernardi, Thes. v. Contrad., p. 300). Piccartus, Isagoge, pp. 290, 
291. Javellus, Ln. Metaph., L. iv. qu. 9. Suarez, Disp. Mctaph., 
Disp. iii., sect. 3, § 5. Stahl, RegulcB Philos., Tit. i. reg. 2. Wolf, 
Ontologia, §§ 27, 29, 56, 71, 498. Ponseca, In. Metaph., L. iv. 
c. iii. qu. 1. et seq., T. I. p. 850. (This principle not first). Tim- 
pier, Metaphgsica, L. ii. c. 8, qu. 15. Derodon, Metaph., p. 76 
(Secundum principium). Lippius, Metaphysica, L. i. c. i., pp. 72, 
75. Chauviu, Lexicon Philosophicum, v. Metaphysica. Scheibler, 
Topica, c. 19. Hurtado de Mendoza, Disp. Metaph., Disp. iii., § 3, 
(Caramuel, Rat. et Real. Phil, § 452, p. 68). 



Whether identical with Principle of Contradiction. 

Affirmative, — 

Javellus, I. c. Mendoza, Disp. Metaph., D. iii. § 3. Leibnitz, 
Oeuvres Philosophiqves, Nouv. Ess., L. iv. c. 2, p. 327. 

Negative, — 

Fonseca, Disp. Met. Disp. iv. c. 3, 9. Suarez, Disp. Metaph., 
Disp. iii. § 3. Stahl, Reg. Phil. Tit. i. reg. 2. 

Whether a valid and legitimate Law. 

Pischer, Logik, § 64 et seq. (Negative). — Made first of all prin- 
ciples by Alexander de Ales, Metaph., xiv. text 9 : " Conceptus 
oranes simplices, ut resolvuntur ad ens, ita omnes conceptus com- 
positi resolvuntur ad hoc principium — De quoUhet affirmatio vel 
negatio." J. Picus Mirandulanus, (after Aristotle), Gonclusiones, 
Opera, p. 90. Philoponus, In An Post. i. f 9 b, (Brandis, 
Scholia, p. 199.) To 8' airau (ftdpai rj aTTOfj^dvai, r) ets to 



248 APPENDIX. 

aS-uvaTov aTToSet^t? Xafx/Savei. Aristotle, An. Post. i. c. 11. § 8. 
'AvTL(f)aai'^ Se avTiBecri'? rjs ovk ean fxera^v KaO" avTTjV. 
An. Post. i. c. 2, § 13. Mera^u di^rt^acreoj? ovk ez^Se^erat 
ovOiv. Metaph. L. iii. c. 7. 'EttcI dvTLcjidcrea)? ovSev dvd 
jxeaov, (fyavepov on iv To1<i evavrioi<^ eVrat to [xera^v. 
Physica, L. v. c. 3, § 5. See also Pos^. An. L. i. c. i. § 4, p. 414 ; 
c. 2, § 13, p. 417; c. 11. § 3, p. 440, (vide Scheibler, Topica, 
c. 19 ; and Mansers Prolegomena, p. 283, on Aristotle.) 

4 Principle of Eeason and Consequent. 

That can be deduced from Principle of Contradiction. 

Wolf, Otitologia, § 70. Baumgarten, Metaphysik, § 18. 

Jakob, Grundriss der allgemeinen Logik und Kritische Ang- 
fangsgrilnde der allgemeinen Metaphysik, p. 38, 3d ed., 1794. 
(See Kiesewetter, I. c.) 

That not to be deduced from Principle of Contradiction. 
Kiesewetter, Allgemeine Logik ; Weitere Auseinandersetzung, 
P. I. ad §§ 20, 21, p. 57 et seq. Hume, On Human Nature, Book 
i. part. iii. § 8. Schulze, Logik, § 18, 5th ed., 1831. 



APPENDIX. 249 

V. 

NEW ANALYTIC OF LOGICAL FOEMS— GENEEAL 
EESULTS— FEAGMENTS. 

(a) Extract from Prospectus of " Essay towards a New 
Analytic of Logical Forms." 

(First publislied in 1846." See above, Vol. I, pp. 144, 244.— Ed.) 



" Now, wJuit has been the source of all these evils, I 'proceed to relate, and shall clearly 
convince those tvho have an intellect and a will to attend, — that a trivial slip in the ele- 
mentari/ j^recepts of a Logical Theory, becomes the cause of mightiest errors in that Theory 
itself." — Galen. {De Temperamentis, 1. i. c. 5.) 



" This New Analytic is intended to complete and simplify the 
old ; — to place the keystone in the Aristotelic arch. Of Abstract 
Logic, the theory, in particular of Syllogism, (bating some improve- 
ments, and some errors of detail), remains where it was left by the 
genius of the Stagirite ; if it have not receded, still less has it ad- 
vanced. It contains the truth ; but the truth, partially, and not 
always correctly, developed, — in complexity, — even in confusion. 
And why ? Because Aiistotle, by an oversight, marvellous certamly 
in him, was prematurely arrested in his analysis ; began his syn- 
thesis before he had fully sifted the elements to be recomposed ; 
and, thus, the system which, abnost spontaneously, would have 
evolved itself into unity and order, he laboriously, and yet imper- 
fectly, constructed by sheer intellectual force, under a load of limi- 
tations and corrections and rules, which, deforming the symmetry, 

a An extract correspouding in part (in the Edinburgh Review) first published 
with that now given from the Prospectus in 1833, the theory of Induction there 
of "Essay towards a New Analytic of maintained proceeds on a thorough 
Logical Forms," is republished in the -Dzs- quantification of the predicate, in aflSr- 
cussions on Philosophy, p. 650. To this mative propositions, 
extract the Author has prefixed the fol- Before 1840, I had, however, become 
lowing notice regarding the date of his convinced that it was necessary to ex- 
doctrine of the Quantification of the Pre- tend the principle equally to negatives ; 
dicate : — " Touching the principle of an for I find, by academical documents, 
explicitly Quantified Predicate, I had, by that in that year, at latest, I had pub- 
1833, become convinced of the necessity licly taught the unexclusive doctrine." 
to extend and correct the logical doctrine — Discussions, p. 650. — Ed. 
upon this point. In the article on Logic 



250 APPENDIX. 

has seriously impeded the usefulness, of the science. This imper- 
fection, as I said, it is the purpose of the New Analytic to supply, 

" In the first place, in the Essay there will be shown, that the 
Syllogism proceeds, not as has hitherto, virtually at least, been 
taught, in one, but in the two correlative and counter wholes 
(Metaphysical) of Comprehension, and (Logical) of Extension ; 
the major premise in the one whole, being the minor premise in 
in the other, &c. — Thus is relieved, a radical defect and vital in- 
consistency in the present logical system. 

" In the second place, the self-evident truth, — That we can only 
rationally deal with what we already understand, determines the 
simple logical postulate, — To state explicitly ivhat is thought ira- 
plicitly. From the consistent application of this postulate, on 
which Logic ever insists, but which Logicians have never fairly 
obeyed, it follows : — that, logically, we ought to take into account 
the quantity, always understood in thought, but usually, and for 
manifest reasons, elided in its expression, not only of the subject, 
but also of the predicate, of a judgment. This being done, and 
the necessity of doing it will be proved against Aristotle and his 
rejieaters, we obtain inter alia, the ensuing results : — 

"1°. Thdii t\iQ 2^'f'^i^dcsignate terms oi a proposition, whether 
subject or predicate, are never, on that account, thought as indefi- 
nite (or indeterminate) in quantity. The only indefinite, is parti- 
cular, as opposed to definite, quantity ; and this last, as it is either 
of an extensive maximum undivided, or of an extensive minimum 
indivisible, constitutes quantity universal, (general), and quantity 
singular, (individual). In fact, definite and indefinite aie the only 
quantities of which we ought to hear in Logic ; for it is only as 
indefinite that particular, it is only as definite that individual and 
general, quantities have any (and the same) logical avail. 

" 2°. The revocation of the two Terms of a proposition to their 
true 7'elation ; a proposition being always an equation of its sub- 
ject and its predicate. 

" 3°. The consequent reduction of the Conversion of Propositions 
from three species to one, — that of Simple Conversion. 

" 4°. The reduction of all the General Laws of Categorical Syllo- 
gisms to a Single Canon. 

" 5°. The evolution from that one canon of all the Species and 
varieties of Syllogism. 



APPENDIX. 251 

" 6°. The abrogation of all the Special Laws of Syllogism. 

" 7°. A demonstration of the exclusive possibility of Three syllo- 
gistic Figures ; and (on new grounds) the scientific and final abo- 
ition of the Fourth. 

" 8°. A manifestation tha,tFigure is an unessential variation in 
syllogistic form ; and the consequent absurdity of Reducing the 
syllogisms of the other figures to the first. 

" 9°. An enouncement oi one Organic Principle iov each Figure. 

" 10°. A determination of the true number of the legitimate 
Moods ; with 

" 11°. Their amplification in number (thirty-six) ; 

u 22°. Their numerical equality under all the figures ; and, 

" J 3°. Their relative equivalence, or virtual identity, throughout 
every schematic difference. 

"14°. That, in the second and third figures, the extremes holding 
both the same relation to the middle term, there is not, as in the 
first, an opposition and subordination betiueen a term major and 
a term minor, mutually containing and contained^ in the counter 
ivholes of Extension and Comprehension. 

" 15°. Consequently, in the second and third figures, there is no 
determinate major and minor premise, and there are two indiffe- 
rent conclusions ; whereas, in the first the premises are determi- 
nate, and there is a single proximate conclusion. 

" 1 6°. That the thi7^d, as the figure in which Comprehension is 
predominant, is more appropriate to Induction. 

"17°. That the second, as the figure in which Extension is pre- 
dominant, is more appropriate to Deduction. 

" 18°. That i\\Q first, as the figure in which. Comprehension and 
Extension are in equilibrium, is common to Induction and Deduc- 
tion, indifferently. 

" In the third place, a scheme of Symbolical Notation will be 
given, wholly different in principle and perfection from those 
which have been previously proposed ; and showing out, in all 
their old and new applications, the propositional and syllogistic 
forms, with even a mechanical simplicity. 

" This Essay falls naturally into two parts. There will be con- 
tained, — in the first, a systematic exposition of the new doctrine 
itself ; in the second, an historical notice of any occasional antici- 



252 APPENDIX. 

pations of its several parts whicli break out in the writings of pre- 
vious philosophers. 

" Thus, on the new theory, many valid forms of judgment and 
reasoning, in ordinary use, but which the ancient logic continued 
to ignore, are now openly recognised as legitimate ; and many 
relations, which heretofore lay hid, now come forward into the 
light. On the one hand, therefore. Logic certainly becomes more 
complex. But on the other, this increased complexity proves only 
to be a higher development. The developed Syllogism is, in effect, 
recalled, from multitude and confusion, to order and system. Its 
laws, erewhile many, are now few, — we might say one alone, — but 
thoroughgoing. The exceptions, formerly so perplexing, have 
fallen away ; and the once formidable array of limitary rules has 
vanished. The science now shines out in the true character of 
beauty, — as One at once and Various. Logic thus accomplishes 
its final destination ; for as ' Thrice-greatest Hermes,' speaking in 
the mind of Plato, has expressed it, — ' The end of Philosophy is 
the intuition of Unity.' " 



(6) — Logic, — Its Postulates. 

(November 1848— See above, Vol. L, p. 114.) 

I. To state explicitly what is thought implicitly. In other 
words, to determine what is meant before proceeding to deal with 
the meaning. Thus in the proposition Me7i are animals, we 
should be allowed to determine whether the term men means all 
or some men, — whether the term animals means all or some ani- 
mals ; in short, to quantify both the subject and predicate of the 
proposition. This postulate applies both to Propositions and to 
Syllogisms.a 

a See (quoted by Wallis, Lorjica, argiimentationis consequentia propter 

p. 291) Aristotle, An. Prior., L. i., c. crypsin] dubitatio fuerit, explenda qua3 

33 (PaciiTS, c. 32, §§ 2, 3, 4, p. 261), desuut ; amputanda quee supersunt ; et 

and Ramus, (from Downam, In P. pars quselibet in locum redigenda situ 

Rami Dialect., L. ii., c. 9, p. 410) : est." [Cf. Ploucquet, Elementa Philo- 

What is understood to be supplied ; sophlm Contemplativcc, § 29, p. 5. Stut- 

[^Ranuis Dial., L. ii., c. 9. " Si qua [de gardise, 1778. " Secundum sensum lo- 



APPENDIX. 253 

II. Throughout the same Proposition, or Immediate (not me- 
diate) Reasoning, to use the same words, and combinations of words, 
to express the same thought a, (that is, in the same Extension and 
Comprehension), and thus identity to be presumed. 

Thus a particular in one (prejacent) proposition of an immediate 
reasoning, though indefinite, should denote the same paH in the 
other. This postulate applies to inference immediate, e. g. Con- 
version. 

Predesignate in same logical unity, ([proposition or syllogism), 
in same sense, both Collective or both Distributive. That one 
term of a proposition or syllogism should not be used distributively 
and another collectively. 

III. And, e contra, throughout the same logical unity, (immediate 
reasoning), to denote and presume denoted the same sense (notion or 
judgment) by the same term or terms./^ 

This does not apply to the different propositions of a Mediate 
Inference. 

IV. (or V.) To leave, if necessary, the thought undetermined, as 
subjectively uncertain, but to deal with it only as far as certain or 
determinable. Thus a whole may be truly predicable, though we 
know only the truth of it as a part. Therefore, we ouglit to be 
able to say some at least when we do not know, and cannot, there- 
fore, say determinately, either that some only or that all is true. 

(January 1850.) 

III. (or IV.) To be allowed, in an immediate reasoning, to de- 

gicum ct;m omni termino jungendum cal proposition, If the Chinese are Ma- 

est signum quantitatis." — Ed.] liometans, they are {some} infidels ; the 

a Tliat words must be used in the word infidel, unless thought in a mean- 
same sense. See Aristotle, Anal. Pr., ing limited to and true of Mahometans, 
L. i., cc. 33, 34, 35, 36, 37, &c. is inept. But if it be so limited, we 

/3 If these postidates (II. and III.) can (contrary to the doctrines of the 

were not cogent, we could not convert, logicians) argue back from the position 

at least not use the converted proposi- of the consequent to the position of the 

tion, (unless the I, were cogent, the con- antecedent, and from the sublation of 

vertenda would be false). All man is the antecedent to the sublation of the 

(an) animal, is converted into iSome consequent, though false. If not gi-anted, 

animal is {all) man. But if the some Logic is a mei'e childish play with the 

animal here were not thought in and vagueness and ambiguities of language 

limited to the sense of the convertend, [Cf. Titius, Ars Gorjitandi, c. xii., § 26. — 

it would be false. So in the Hypotheti- Ed.] 



254 APPENDIX. 

note, that another part, other, or some, is used in the condusion, 
from what was in the antecedent. Inference of Sub-contrariety. 

That the some, if not otherwise qualified, means some only, — 
this by presumption. 

That the Term (Subject, or Predicate) of a Proposition shall be 
converted with its quantity unchanged, i. e. in the same extension. 
This violated, and violation cause of error, and confusion, ^oper 
accidens, for the real terms compared are the quantified terms, 
and we convert only the terms compared in the prejacent or con- 
vertenda. 

That the same terms, apart from the quantity, i. e. in the same 
comprehension, should be converted. As before stated, such terms 
are new and different. No Contraposition, for contraposition is only 
true in some cases, and even in these it is true accidentally, not by 
conversion, but through contradiction ; i. e. same Comprehension. 

That we may see the truth from the necessary validity of the 
logical process, and not infer the validity of the logical process 
from its accidental truth. Conversion j;e?' accidens, and Contra- 
position, being thus accidentally true in some cases only, are logi- 
cally inept, as not true in all. 

To translate out of the complexity, redundance, deficiency, of 
common language into logical simplicity, precision, and integrity." 

(December 1849). 

As Logic considers the form and not the matter, but as the form 
is only manifested in application to some matter, Logic postulates 
to employ any matter in its examples. 

(January 1850). 

That we may be allowed to translate into logical language the 
rhetorical expressions of ordinary speech. Thus the Exceptive and 
Limitative propositions in which the predicate and subject are pre- 
designated, are to be rendered into logical simplicity. 

a See above, p. 252, note o. — Ed. 



APPENDIX. 255 

(May 1850). 

As Logic is a formal science, and professes to demonstrate by- 
abstract formulfe, we should know, therefore, nothing of the no- 
tions and their relations exce23t ex facie of the propositions. This 
implies the necessity of overtly quantifying the predicate. 



(c) — Quantification of Predicate, — Immediate 
Inference, — Conversion, — Opposition." 

(See above, Vol. I., pp. 244, 262.) 

We now proceed to what has been usually treated under the 
relation of Propositions, and previously to the matter of Infer- 
ence altogether ; but which I think it would be more correct to 
consider as a species of Inference, or Eeasoning, or Argumenta- 
tion, than as merely a preparatory doctrine. For in so far as these 
relations of Propositions warrant us, one being given, to educe 
from it another, — this is manifestly an inference or reasoning. 
Why it has not always been considered in this light, is evident. 
The inference is immediate ; that is, the conclusion or second pro- 
position is necessitated directly and without a medium, by the first. 
There are only two propositions and two notions in this species of 
argumentation ; and the logicians have in general limited reason- 
ing or inference to a mediate eduction of one proposition out of 
the correlation of two others, and have thus always supposed the 
necessity of three terms or collated notions. 

But they have not only been, with few exceptions, unsystematic 
in their procedure, they have all of them, (if I am not myself 
mistaken), been fundamentally erroneous in their relative doctrine 

There are various Immediate Inferences of one proposition from 
another. Of these some have been wholly overlooked by the lo- 
gicians ; whilst what they teach in regard to those which they do 
consider, appears to me at variance with the truth. 

I shall make no previous enumeration of all the possible species 

« Appendix (c),from p. 255 to p. 274, of Conversion as given above, vol. i., p. 
was usually delivered by the author as a 262. — Ed. 
Lecture, supplementary to the doctrine 



256 APPENDIX. 

of Immediate Inference ; but shall take them up in this order : — 
I shall consider, 1°, Those which have been considered by the logi- 
cians; and, 2°, Those which have not. And in treating of the 
first group, I shall preface what I think the true doctrine by a 
view of that whicli you will find in logical books. 

The first of these is Conversion. When, in a categorical propo- 
sition, (for to this we now limit our consideration), the Subject and 
Predicate are transposed, that is, the notion which was previously 
the subject becomes the predicate, and the notion which v/as pre- 
viously the predicate becomes the subject, the proposition is said 
to be converted." The projDosition given, and its product, are to- 
gether called the judicia conversa, or propositiooies converses, 
whicli I shall not attemj)t to render into English. The relation 
itself in which the two judgments stand, is called conversion, re- 
ciprocation, transposition, and sometimes obversion, (conversio, 
recip>rocatio, transpositio, ohversio.) 

The original or given proposition is called the Converse, or 
Converted, sometimes the Prcejacent, Judgment, {judicium, or 
propositio, conversum, conversa, prcejacens) ; the other, that into 
which the first is converted, is called the Converting, and some- 
times the Subjacent, Judgement, {propositio, or jud. convertens, 
subjacens). It would be better to call the former the Convertend, 
{p)r. convertenda), the latter the Converse, {yr. conversa). This 
lauouao-e I shall use.'^ 



a [Definitions of conversion in general. [Names for the two propositions in 

'ApTiaTpo(j)r] iffTiv t(TO(rTpo(pr] ris, Phil- Conversion. 

oponus, (or Ammonius); In An. Pr., i. I. Name for the two coiTelative j^ro- 

c. 2, f. lib. So Magentinus, /?i 4 m.. Pr. positions — Conversa, Twesteu, ioy«X-, § 

i. c. 2, f. 3 b. Anonymus, De Syllo- 87, Contraposita, /(/. ibid, 

gismo, f. 42 b. UpoTaa-ecos avTi.(rrpo(p7} II. Original, or Given Proposition. 

ecTTi KOLvwvia 5to TTpoTaffiwv Kara rovs a) 7] Trpo7]yovfj.evr], irpo/cei/xeVrj, avTiarpe- 

'6povs a,vdira\iv ridefj-evovs, fieTO, rov (Tvv- (poixevri TrpSraais — Cf. Strigelius, In 

a\r]Bfveiv. Alexander, /;; An. Pr. i. c. 4, Miianchth. Erot. Dial., L. ii., p. 581. 

f . 15 b. See the same in different words, 'AvTia-rpfipovaai irporaffeis, Philopon- 

by Philoponus, (Ammouius), In An. Pr., \is, (quoted by Wegelin, /. c.) 

i. c. 2, f. 11 b., and copied from him by b) Conversa (= Convertenda) vulgo. 

Magentinus, In An. Pr., f. 3 b. Cf. Scotus, Qucvstmies in An. Prior., i. 

Boethius, Opera, Introductio ad Syllo- q. 12. Corvinus, Instit. Phil., § 510. 

gismos, p. 574. Wegelin, in Gregorii Richter, Be Conversione, 1740. Halso 

Aneponymi Phil. Syntag. (circa 1260), Magdeb. Baumgarten, Logica, § 278. 

L. v., c. 12. p. 621. Nicephorus Blem- 1J\vich.,In»tit.Log. e<Jfe<.,§182,p. 188. 

midas, Epit. Log., c. 31, p. 221.] c) Convertibilis (rare). 

^ See above, vol. i., p. 262. — Ed. d) Convertens, Micraelius, Lex. Phil. v. 



APPENDIX. 257 

Such is the doctrine touching Conversion, taught even to the 
present day. This in my view is beset with errors ; but all these 
errors originate in two, as these two are either the cause or the 
occasion of every other. 

The First cardinal error is, — That the quantities are not con- 
verted with the quantified terms. For the real terms compared in 
the Convertend, and which, of course, ought to reappear without 
change, except of place, in the Converse, are not the naked, but the 
quantified terms. This is evident from the following considerations : 

J °, The Terms of a Proposition are only terms as they are terms 
of relation ; and the relation here is the relation of comparison. 

2°, As the Prepositional Terms are terms of comparison, so they 
are only compared as Quantities, — quantities relative to each other. 
An Aflirmative Proposition is simply the declaration of an equation, 
a Negative Proposition is simply the declaration of a non-equation, 
of its terms. To change, therefore, the cpiantity of either, or of 
both Subject and Predicate, is to change their correlation, — the 
point of comparison ; and to exchange their quantities, if different, 
would be to invert the terminal interdependence, that is, to make 
the less the greater, and the greater the less. 

3°, The Quantity of the Proposition in Conversion remains always 
the same ; that is, the absolute quantity of the Converse must be 
exactly equal to that of the Convertend. It was only from over- 
looking the quantity of the predicate, (the second error to which we 

Converslo. Twesten, Lof/il\, § 87. An- a) t] avna-rpffova-a. See Strigelius, loc. 
tecedens, Scotus, I. r. Strigelius, /. c. cit. 

e) PiU'jacens, Scheibler, Opera Lor/ira, h) Convertens, Subjacens, Scotus, Quws- 
I)e Propositionihus, Pars. iii. c. x. p. tiones, In An. Prior, i. 9, 24, f. 276, 
479. et passim. Krug, Lur/il; § 65, p. 205, 

f) Exposita, Akb'ich, Comp., L. i. c. 2. and logicians in general. 

Whately, Zor/t'c, p. 69. Propositio ex- c) Conversa, Boethius, Opera, In trod. 

posita, or exponens, quite different as ad Si/ll., -pp. 575 ef seq., 587 et scq.; 

used by Logicians, v. Scliegkius, /// Melanchthon, Z;>o<e»iate, L. ii. jd. 681, 

Arist. Orcj. 162 (and above, vol. i., p. and Strigelius, ad lor. Micraelius, 

263.) leoc. Pfiil., 7\ Conrersio. Noldius, 

g) Convertenda, Corvinus, loc. cit. Rich- Logica Recognita, p. 263, says that 
ter, loc. cit. the first should more probablj^ be 

h) Contraponens, Twesten, Ihid. called Convertibilis, or Convei-tenda, 

i) Prior, Boethius, De Syllog. Categ. L. and the second Conversa. 

I. 0/Jera, p. 588. d) Conversum, Twesten, loc. cit. 

k) Principium, Darjes, Via ad Verita- e) Contrapositum, Id. ihid. 

tern, § 234. f) Conclusio, Darjes, Via ad Veritatcm, 

III. Product of Conversion. § 234. 

VOL. II. R 



258 APPENDIX. 

sTiall immediately advert), that two propositions, exactly equal in 
quantity, in fact the same proposition, perhaps, transposed, were 
called the one universal, the other jmrticulm', by exclusive refer- 
ence to the quantity of the subject. 

4°, Yet was it of no consequence, in a logical point of view, 
which of the notions collated were Subject or Predicate ; and their 
comparison, with the consequent declaration of their mutual incon- 
clusion or exclusion, that is, of affirmation or negation, of no more 
real difference than the assertions, — London is four hundred 
miles distant from Edinburgh, — Edinburgh is four hundred 
miles distant from London. In fact, though logicians have 
been in use to place the subject first, the predicate last, in their 
examples of propositions, this is by no means the case in ordinary 
language, where, indeed, it is frequently even difficult to ascertain 
which is the determining and which the determined notion. Out 
of logical books, the predicate is found almost as frequently before 
as after the subject, and this in all languages. You recollect the 
first words of the First Olyminad of Pindar, ''ApicTTOv ixev vSop, 
"Best is water ;" and the Vulgate, (I forget how it is rendered in 
our English translation), has, "Magna est Veritas, et prsevalebit." « 
Alluding to the Bible, let us turn up any Concordance under any 
adjective title, and we shall obtain abundant proof of the fact. As 
the adjective great, magnus, has last occurred, let us refer to 
Cruden under that simple title. Here, in glancing it over, I find — 
" Great is the wrath of the Lord — Great is the Lord and greatly to be 
praised — Great is our God — Great are thy works — Great is the Holy 
One of Israel — Great shall be the peace of thy children — Great is thy 
faithfulness — Great is Diana of the Ephesians — Great is my boldness 
— Great is my glorying — Great is the mystery of godliness," &c. 

The line of Juvenal, 

"Nobilitas sola est atqne imica virtus," 

is a good instance of the predicate being placed first. 

The Second cardinal error of the logicians is, the not considering 
that the Predicate has always a quantity in thought, as much as 
the Subject ; although this quantity be frequently not explicitly 
enounced, as unnecessary in the common emijloyment of language ; 

a III. Esdras iv. 41 : " Magna est veri- (I. Esdras iv. 41), " Great is truth, and 
tas et prsevalet." In the English version, mighty above all things." — Ed. 



APPENDIX. 259 

for tlie determining notion or predicate being always thought as at 
least adequate to, or co-extensive with, the subject or determined 
notion, it is seldom necessary to express this, and language tends 
ever to elide what may safely be omitted. But this necessity 
recurs, the moment that, by conversion, the predicate becomes the 
subject of the proposition ; and to omit its formal statement is to 
degrade Logic from the science of the necessities of thought, to an 
idle subsidiary of the ambiguities of speech. An unbiassed con- 
sideration of the subject will, I am confident, convince you that 
this view is correct, 

1°, That the jjredicate is as extensive as the subject is easily 
shown. Take the proposition, — All animal is man, or, All ani- 
mals are men. This we are conscious is absurd, though we make 
the notion man or men as wide as possible ; for it does not mend 
the matter to say, — All animal is all man, or. All animals are 
all men. We feel it to be equally absurd as if we said, — All man 
is all animal, or. All men are all animals. Here we are aware 
that the subject and predicate cannot be made coextensive. If we 
would get rid of the absurdity, we must bring the two notions into 
coextension, by restricting the wider. If we say — Man is animal, 
{Homo est animal), we think, though we do not overtly enounce 
it, All man is animal. And what do we mean here by animal ? 
We do not think, — All, but Some, animal. And then we can 
make this indifferently either subject or predicate. We can think, 
— we can say. Some animal is man, that is, Seine or All Man ; 
and, e converso, — Man (some or all) is animal, viz. so7ne animal. 

It thus appears that there is a necessity in all cases for thinking 
the predicate, at least, as extensive as the subject. Whether it be 
absolutely, that is, out of relation, more extensive, is generally of 
no consequence ; and hence the common reticence of common 
language, which never expresses more than can be understood, — 
which always, in fact, for the sake of brevity, strains at ellipsis. 

2°, But, in fact, ordinary language quantifies the Predicate so 
often as this determination becomes of the smallest import. This 
it does either directly, by adding all, some, or their equivalent pre- 
designations, to the predicate ; or it accomplishes the same end 
indirectly, in an exceptive or limitative form. 

a) Directly, — as Peter, John, James, &c., are all the Apostles 
— Mercury, Venus, &c., are all the planets. 



260 



APPENDIX. 



b) But this is niore frequently accomplished indirectly, by the 
equipollent forms of Limitation or Inclusion, and Exception. « 

For example, by the limitative designations, alone or only, we 
say, — God alone is good, which is equivalent to saying, — God is all 
good, that is, God is all that is good ; Virtue is the only nobi- 
lity, that is. Virtue is all nohle, that is, all that is nohlefi The 
symbols of the Catholic and Protestant divisions of Christian- 
ity may afford us a logical illustration of the jioint. The Ca- 
tholics say, — Faith, Hope, and Charity alone justify ; that is, the 
three heavenly virtues together are all justifying, that is, all that 
justifies; omne justificans, justum faciens. The Protestants 
say, — Faith alone justifies ; that is, Faith, which they hold to 
comprise the other two virtues, is all justifying, that is, all that 



a By the logicians this is called simply 
Exclusion, and the particles, tantum, &c., 
particuke exclasivce. This, I think, is 
inaccurate ; for it is inclusion, limited by 
an exclusion, that is meant. — [See Schei- 
bler, Opera Logica, P. iii., c. vii., tit. 3, 
p. 457 et seq.] 

i8 (February 1850.) On the Indirect 
Predesignation of the Predicate by what 
are called the Exclusive and Exceptive 
praficles. 

Names of the particles. 

Latin, — iimis, unicus, unice ; solus, 
solum, solummodo, tantum, tantummodo ; 
duntaxat ; prcecise ; ad(equate. Nihil 
prceter, — prwterquam, — ni nisi non. 

English, — one, 07ily, alone, exclusively, 
precisely, just, sole, solely, nothing but, 
not except, not beyond. 

I. These particles annexed to the Sub- 
ject predesignate the Predicate univer- 
sally, or to its whole extent, denying its 
particularity or indefinitude, and defi- 
nitely limiting it to the subject alone. 
As, Man alonephilosophhes, (though not 
all do). The dog alone barks, or, dogs 
alone bark, (though some do not). Man 
only is rational, or No animal but man is 
rational. Nothing but rational is risible. 
Of material things there is iwthing living 
(but) not organised, and nothing organ- 
ised not living. God alone is to be wor- 
shipped. God is the single, — sole object 



of worship. 'Some men only are elect. 

II. Annexed to the Predicate, they 
limit the subject to the predicate, but 
do not define its quantity, or exclude 
from it other subjects. As, Peter only 
plays. The sacraments are only tivo. 
The categories are only ten. John drinks 
only loater. 

III. Sometimes the particles eole, 
solely, single, alone, only, &c., are an- 
nexed to the Predicate as a predesigna- 
tion tantamount to all. As, God is the 
single, — one, — alone, — only, — exclusive, 
— adequate, object of worship. 

On the relation of Exclusive proposi- 
tions to those in which the predicate is 
predesignated, see Titius, Ars Cogitandi, 
c. vi. §§ QQ, 67. Hollman, Philosophia 
Bationalls, § 475. Kreil, Handbuch der 
Logik, § 62. Derodon, Logica Restituta, 
De Enunciatione, c. v. p. 569 et seq. 
Keckerman, Systema Logicce, lib. iii., c. 
11. Opera, t. i. p. 763. 

The doctrine held by the logicians as 
to the exclusum prcedicatum, exchisum 
subjectum, and exclusum signum, is er- 
roneous. — See Scheibler, Opera Logica, 
P. iii., c. vii., tit. 3, p. 457 et seq. Jac. 
Thomasius, Erotem. Log., c. xxx. p. 67 et 
seq. [Cf. Fonseca, Instit. Dial., L. III. 
c. 23. For a detailed exposition of this 
doctrine by Scheibler, see below, p. 261, 
note o. — Ed.] 



APPENDIX. 



261 



justifies ; omne justificans. In either case, if we translate the 
watchwords into logical simplicity, the predicate appears prede- 
signated. 

Of animals man alone is rational ; that is, Man is all rational 
animal. What is rational is alone or only risible ; that is, All 
rational is all risible, &c. 

I now pass on to the Exceptive Form. To take the motto over- 
head, — " On earth there is nothing great but man." What does 
this mean ? It means, Man — is — all earthly great. — Homo — est 
— omne magnum terestre. And the second clause — "In man 
there is nothing great but mind," — in like manner gives as its 
logical equipollent — Mind — is — all humanly great, that is, all that 
is great in man. {Mens est omne magnum humanum.)a 

We ought, indeed, as a corollary of the postulate already stated, 
to require to be allowed to translate into equivalent logical terms 



a Vide Scheibler, Opera Logica, P. iii. 
c. vii. pp. 458, 460, where his examples, 
with the exposition of the Logician.?, 
may be well contrasted with mine. 

[Scheibler, after referring to the 
Parva Logicalia of the schoolmen, a.s 
containing a proposed supplement of 
the doctrines of Aristotle, pi-oceeds to 
exjjound the Propositiones Exponihiles 
of those treatises. " Exclusiva enun- 
ciatio est, qua; habet particulam ex- 
clusivam, ut. Solus homo est rationahs. 

Pori'o exclusivaj ennn- 

ciationes sunt duplicis generis. Alise 
sunt exclusivse prsedicati : alife exclu- 
sivae subjecti ; hoc est, in aliis parti- 
cula exclusiva excludit a subjecto, in 
aliis excludit a prgedicato, veluti ha3c 
propositio exclusiva est : Deus tantum 
est iminortalis . Estque exclusiva a sub- 
jecto, hoc sensu, Deus tantum, et non 

homo vel lapis, &c Omnes 

propositiones exclusiva; ambiguo; sunt, 
si habeaut particulam exclusivam, post 
subjectum propositionis, ante vinculum, 
ut erat in proposito exemplo. Carent 
autem propositiones exclusivse ilia am- 
biguitate, si vel exclusiva particula, pon- 
atur ante subjectum propositionis, vel 
etiam sequatur copulam. Ibi enim 
indicatur esse propositio exclusiva sub- 



jecti, ut, solus homo discurrit. Hie au- 
tem indicatur, esse propositio exclusiva 
prtcdicati, ut, Sacramenta Novi Testa- 
meiiti sunt tantum duo. Pnedicamenta 
tantmn decern." 

Scheibler then proceeds to give the 
following general and special rules of 
Exclusion : — 

" I. Generaliter tenendum est, quod 
allter sint exponendce exclusivce a prcedi- 
cato, et aliter exclusivce a subjecto. 

" II. Exclusiva propositio non excludit 
concomitantia. 

"III. Omnis exclusiva resolvitur induas 
simplices, altefam affirmatam, alteram 
negatam. Atque hoc est quod vulgo 
dicitur, quod omnis exclusiva sit hypo- 
thetica. Hypothetica enim projjositio 
est qua3 includit duas alias in virtute, 
vel disi^ositioue sua. Veluti hsec, Solus 
homo est rationalis, aequivalet his dua- 
bus, Homo est rationalis, et q^iod non est 
homo, non est rationale. Et in specie, 
Bestia non est rationalis. Planta non 

est rationalis Atque 

hse dua; propositiones vocantur expon- 
entes, sicut propositio exclusiva dicitur 
exjMnibilis. 

" Speciales autem regulae explicandi 
exclusivas sunt octo: sicut et octo sunt 
genei'a locutionum exclusivarum. 



262 



APPENDIX. 



tlie rhetorical enouncements of common speech. We should not 
do as the logicians have been wont, — introduce and deal with these 
in their grammatical integrity; for this would be to swell out and 
deform our science witli mere grammatical accidents ; and to such 
fortuitous accrescences the formidable volume, especially of the 
older Logics, is mainly owing. In fact, a large proportion of the 
scholastic system is merely grammatical. 

3°, The whole doctrine of the non-quantification of the predicate 
is only another example of the passive sequacity of the logicians. 
They follow obediently in the footsteps of their great master. We 
owe this doctrine and its prevalence to the precept and authority 
of Aristotle. He prohibits once and again the annexation of the 
universal predesignation to the predicate. For why, he says, such 
predesignation would render the proposition absurd ; giving as his 
only example and proof of this, the judgment — All man is all 
animal. This, however, is only valid as a refutation of the ridicu- 
lous doctrine, held by no one, that any predicate may be universally 



"I. Proposltio exclusiva universalis af- 
Jirmativa, cujus si[/num non ner/atur, ut, 
Tantum omnis homo cuiYit, exponitur 
sic, Omnis homo currit, et nihil aliud ab 
homine currit. Vocari solet ha3C exposi- 
tio Pater, quia prior ejus pars est uni- 
versalis afRrmativa, quod notat A. Et, 
alterse pars est universalis negativa, quod 
indicat in posteriori syllaba litera E. 

" II. Propositio particvlaris, vel inde- 
finita affirmativa, in qua signum non 
negatur, ut Tantum homo currit, exponi- 
tur sic, Uomo currit, et nihil aliud ab 
homine currit. Vocatur hsec expositio, 

NiSE. 

" III. Propositio exclusira, in qua sig- 
num non negatur, universalis negativa, ut, 
Tantum nullus homo curnt, exponitur sic, 
Nullus homo currit, et quodlibet aliud ab 
homine currit, vocatur, Tenax." 

" IV. Exclusiva cujus signum non ne- 
gatur particular is vel indefinita negativa, 
ut, Tantum homo non currit, exponitur 
sic, Homo non currit, et quodlibet aliud 
ab homine currit, vocatur, Storax. 

"V. Exclusiva, in qua signum negatur, 
affirmativa et universalis, ut, Non tan- 
tum omnis homo currit, exponitur sic, 



Omnis homo cuirit, et aliquod aliud ab 
homme currit, vocatur, Canos. 

" VI. In qua signum negatur, existens 
universalis affirmativa, ut, Non tantum 
nullus homo currit, sic exponitur, Nidlus 
homo currit, et aliquid aliud ab homine 
non currit, vocatur. Fecit. 

" VII. Exclusiva, in qua signum nega- 
tur, existens particularis affirmativa, ut, 
Non tantum aliquis homo currit, expositur 
sic, Aliquis homo currit, aliquid aliud 
ab homine currit, vocatur, Pilos, 

" VIII. Negativa particularis exclu- 
sive propositiones, cujus signum negatur, 
ut, Non tantum aliquis homo non currit, 
exponitur sic, A liquis homo non currit, et 
aliquid aliud ab homine non cwTit,yoca- 
tur. Nobis. 

" Differentia autem propositionis ex- 
clusiva3 et exceptivue est evideus. Nempe 
exclusiva prajdicatum vendicat uni sub- 
jecto, aut asubjecto excludit alia prajdi- 
cata, ut, S'ulus Dcus bonus est. Exceptiva 
avitem statuit universale subjectum, in- 
dicatque aliquid contiueri sub isto uni- 
versali, de quo non dicatur prtcdicatum, 
ut, Onme animal est irrationale, i:)rwtcr 
hominem." — Ed.] 



APPENDIX. 2G3 

quantified ; for, to employ his own example, what absurdity is 
there in saying that some animal is all man ? Yet this non- 
sense, (be it spoken with all reverence of the Stagirite), has imposed 
the precept on the systems of Logic down to the present day. 
Nevertheless, it could be shown by a cloud of instances from the 
Aristotelic writings themselves, that this rule is invalid ; nay 
Aristotle's own doctrine of Induction, which is far more correct 
than that usually taught, proceeds upon the silent abolition of the 
erroneous canon. Tlie doctrine of the logicians is, therefore, 
founded on a blunder ; which is only doubled by the usual aver- 
ment that the predicate, in what are technically called i^eciprocal 
propositions, is taken universally vi materia: and not viformce. 

But, 4°, The non-quantification of the predicate in thought is 
given up by the logicians themselves, but only in certain cases 
where they were forced to admit, and to the amount which they 
could not possibly deny. The predicate, they confess, is quanti- 
fied by particularity in affirmative, by universality in negative, 
propositions. But why the quantification, formal quantification, 
should be thus restricted in thought, they furnish us with no valid 
reason. 

To these two errors I might perhaps add as a third, the confu- 
sion and perj^lexity arising from the attempt of Aristotle and the 
logicians to deal with indefinite, (or, as I would call them, indesig- 
nate), terms, instead of treating them merely as verbal ellipses, to 
be filled up in the expression before being logically considered ; 
and I might also add as a fourth, the additional comjilexity and 
perplexity introduced into the science by viewing propositions, 
likewise, as affected by the four or six modalities. But to these 
I shall not advert. 

These are the two principal errors which have involved our 
systems of Logic in confusion, and prevented their evolution in 
simplicity, harmony, and completeness ; — which have condemned 
them to bits and fragments of the science, and for these bits and 
fragments have made a load of rules and exceptions indispensable, to 
avoid falling into frequent and manifest absurdity. It was in 
reference to these two errors chiefly, that I formerly gave you as a 
self-evident Postulate of Logic — " Explicitly to state what has been 
implicitly thought ; " in other words, that before dealing logically 
with a proposition, we are entitled to understand it, that is, to 



204 APPENDIX. 

ascertain and to enounce its meaning. This quantification of the 
predicate of a judgment, is, indeed, only tlie beginning of the appli- 
cation of the Postulate ; but we shall find that at every step it 
enables us to cast away, as useless, a multitude of canons, which 
at once disgust the student, and, if not the causes, are at least the 
signs, of imperfection in the science. 

I venture then to assert, that there is only one species of Con- 
version, and that one thorough-o-oino; and self-sufficient. I mean 
Pure, or Simple Conversion. The other species, — all are admitted 
to be neither thorough-going nor self-sufficient, — they are in fact 
only other logical processes, accidentally combined with a transpo- 
sition of the subject and predicate. The conversio per accidens 
of Boethius, as an Ampliative operation, has no logical existence ; 
it is material and precarious, and has righteously been allowed to 
drop out of science. It is now merely an historical curiosity. As 
a Restrictive operation, in which relation alone it still stands in our 
systems, it is either merely fortuitous, or merely possible through 
a logical process quite distinct from Conversion, I mean that of 
Eestriction or Subaltei-nation, which will be soon explained. Con- 
verslo per contraposltioneiii is a change of terras, — a substitution 
of new elements, and only holds through contradiction," being just 
as CTOod without as with conversion. The Contino-ent Conversion 



a. [See Ai'istotle, Tupica, L. ii. c. With the single exce^jtiuii of E u E (A 

8. Scotus, Bauues, Mendoza, silently n A) the other seven propositions may 

following each other, have held that be converted by Counterposition under 

contraposition is only mediate, infinita- the following rule, — ' Let the terms be 

tion, requiring Constantia, &c. Wholly infinitated and transposed, the predesig- 

wrong. See Arriaga. — Curms Ph'doso- nations remaining as before.' 

phicus, D. II. s. 4. p. 18. [" Observau- With the two additional exceptions 

dum est prtedictas consequentias (per of the two convertible propositions, 

contrapositionem) malas esse et insta- A f I, and I f A, the infinitated propo- 

biles, nisi accesserit alia jjropositio in sitions hold good without the transposi- 

antecedenti qune impartit existentiam tion of the terms, 

subjecti fousequentis. Tunc enim firma Rule for Infinite Prejaceuts given, 

erit consequentia, e.g. Omnis homo e^t With the single exception of n If n I, 

albas et non album est, ergo omne non (nE = n = nE being impossible), the 

album est non homo. Alioquin si con- other six propositions may be converted 

stantiam illam non posueris in antece- by Counterposition under the following 

denti, instabitur illi consequentiae in rule, — ' Let the terms be uninfinitated 

eventu, in quo nihil sit non album, et and transposed, the predesignatious re- 

omnis homo sit albus." Bannes, Inst'it. maining as before.' 

Min. Dial. L. vi. c. 2, p. 530. — Ed.] Contraposition is not exphcitly evolved 

Rule for Finite Prejacents given. by Aristotle in Prior Anabjtics, but is 



APPENDIX. 



2G5 



of tlie lower Greeks " is not a conversion, — is not a logical process 
at all, and has been worthily ignored by the Latin world. But 
let us now proceed to see that Simple Conversion, as I have 
asserted, is thorough-going and all-sufficient. Let us try it in 
all the eight varieties of categorical propositions. But I shall 
leave this explication to yourselves, and in the examination will 
call for a statement of the simple conversion, as aj)plied to all the 
eight propositional forms. 

It thus appears, that this one method of conversion has every 
advantage over those of the logicians. 1°, It is Natural ; 2°, It 
is Imperative ; 3°, It is Simple ; 4°, It is Direct ; 5°, It is Pre- 
cise ; 6°, It is Thorough-going : "Whereas their processes are — 1°, 



evolved from his Tuples, L. ii. cc. 1, 8, 
alibi. De Interpretatione, c. 14. See 
Conimbricenses, In Arist. Dial., An. 
Prior., L. I. q. i. p. 271. Bannes, Instit. 
Minm^s Bialectlcfv, L. v. c. 2, p. 532. 
Burgersdicius, Instit. Log. L. i. c. 32. 

First explicitly enounced by Averroes 
according to Molinaeus, {Ekmenta Lorji- 
ca, L. i. c. 4, p. 54). I cannot find any 
notice of it in Averroes. He ignores it, 
name and thing. It is in Anonymus, 
De Syllogismo, f. 42 b., in Nicephorus 
Blemmidas, Epit. Log., c. xxxi. p. 222 ; 
but long before him Boethius has all 
the kinds of Conversion, — Simplex, Per 
Acciclens, et Per Oppositionem {Intro- 
ductio ad Sijllogismos, p. 576), what he 
calls Per Contrapositionem, (De Syllo- 
f/lsmo Categorico, L. i. 589.) Is he the 
inventor of the name ? It seems so. 
Long before Boethius, Apuleius, (in 
second century), has it as one of the five 
species of Conversion, but gives it no 
name — only descriptive, see Dellahittid. 
Doct. Plat., L. lii. p. 33. Alexander, In 
An. Pr., i. c. 2, f. 10 a, has it as of pro- 
positions, not of terms, which is con- 
version absolutely. Vide Philoponus, In 
An. Pr., I. f. 12 a. By them called avTi- 
CTpocp)) (Tvv ai/TLOecet. So Magentinus, 
In An. Prior., i. 2, f. 3 b. 

That Contraposition is not properly 
Conversion — (this being a species of con- 
sequence) — an sequipoUence of pi'oposi- 
tions, not a conversion of their terms. 



Noldius, Logica Recognita, c. xii. p. 
299. Crakanthorpe, Logica, L. iii. c. 
10, p. 180. Bannes, Instit. Min. Dial., 
L. V. c. 2, p. 530. Eustachius, Summa 
Philosophice, Lo/jica, P. II. tract, i. q. 3, 
p. 104. Herbart, Lehrhuch der Logik, 
p. 78. Scotus, Qiicestiones, In An. Prior., 
L. i. q. 15, f. 258 b. Chauvin, v. Con- 
'versio. Isendoorn, Cursus Logicus,^). 308. 

That Contraposition is useless and 
^lerplexing. See Chauvin, v. Conversio. 
Arriaga, Cursus, PhilosopKicus, p. 18. 
Titius,^ rs Cogitandi, c. viii. § 19 e< seq. 
D'Abra de Raconis, Tot. Phil. Tract., 
Logica, ii. q. 4, p. 315. Bannes, Instit. 
Min. Dial, Yi. 529.] 

o [Blemmidas.] [Epitome Logica, c. 
31, p. 222. The following extract 
will explain the nature of this con- 
version. 'H 5' iv irpoTo.ffea'i yivo^lvi) 
avTLarpocp^, f] r^v fiev Ta^iv tuv Spccu 
(pvAarrei, rhy avrhv rripovaa Karriyopov- 
fxsvov KoL rhv axnhv inroKeiixevov • fi6vi]V 
Se TT]V 7roj(5T7jTa fiera^aWfi, Troiovffa t^jv 
a,iTo(parLKi)v Trpuraaiv Kara(pa.riKi]V, koli 
KaratpaTLKT^v airo(paTLKriv. Kal KeyeTai 
avTY] iySexo/^^vri avTiarpocpi], ws tTri ix6vris 
TTjS ivSexo/J-evvs v\7]s avvLaTaixivf) • oTov, 
TLS avOpooTTos \overai, tis ^.^OpooTvos ov \ov- 
erai • avrr] S' ovk av ety) Kvpioos avTt- 
ffTpotp-f). This so-called contingent con- 
version is in fact nothing more than the 
assertion, repeated by many Latin logi- 
cians, that in contingent matter subcon- 
trary propositions are both true. — Ed.] 



266 APPENDIX. 

Unnatural ; 2°, Precarious ; 3°, Complex ; 4°, Circuitous ; 5°, Con- 
fused ; 6°, Inadequate : breaking down in each and all of their 
species. The Greek Logicians, subsequent to Aristotle, have well 
and truly said, dpTLcrTpocfut] ecxTiv IcTocrTpo^rj rt? " omnis conversio 
est ajquiversio" * that is, all conversion is a conversion of equal into 
equal ; and had they attended to this principle, they would have 
developed conversion in its true unity and simplicity. They would 
have considered, 1°, That the absolute quantity of the proposi- 
tion, be it convertend or converse, remains always identical ; 2"*, 
That the several quantities of the collated notions remain always 
identical, the whole change being the transjjosition of the quanti- 
fied notion, which was in the subject place, into the place of pre- 
dicate, and vice versa. 

Aristotle and the logicians were, therefore, wrong; 1°, In not 
considering the proposition simply as the complement, that is, as 
the equation or non-equation, of two compared notions, but, on the 
contrary, considering it as determined in its quantity by one of 
these notions more than by the other. 2°, They were wrong, in 
according too great an imj)ortance to the notions considered as pro- 
positional terms, that is, as subject and predicate, independently 
of the import of these notions in themselves. 8°, They were 
wrong, in according too preponderant a weight to one of these 
terms over the other ; but difierently in different parts of the 
system. For they were wrong, in the doctrine of Judgment, in 
allowing the quantity of the proposition to be determined exclu- 
sively by the quantity of the subject term ; whereas they were 
wrong, as we shall see, in the doctrine of Reasoning, in considering 
a syllogism as exclusively relative to the quantity of the predicate 
(extension). So much for the theory of Conversion. Before con- 
cluding, I have, however, to observe, as a correction of the preva- 
lent ambiguity and vacillation, that the two j)roi30sitions of the 
process together might be called the convertent or converting, (pro- 
2)ositiones convertentes) ; and whilst of these the original proposi- 
tion is named the convertend [propositio convertenda), its product 
would obtain the title oi converse, converted, (propositio conversd).^ 

The other species of Immediate Inference will not detain us 
long. Of these, there are two noticed by the logicians. 

a See above, p. 256. — Eu. fi See above, vol. i. p. 262. — Ed. 



APPENDIX. 2G7 

Tlie first of these, EquipoUence, (cequipoUentid), or, as I would 
term it, Double Negation, is deserving of bare mention. It is of 
mere grammatical relevancy. The negation of a negation is tanta- 
momit to an affirmation. B is not not-A, is manifestly only a 
roundabout way of saying B is A ; and, vice versa, we may express 
a position, if we perversely choose, by sublating a sublation. The 
immediate inference of Equipollence is thus merely the grammati- 
cal translation of an affirmation into a double negation, or of a 
double negation into an affirmation. Non-nullus and Non-nemo^ 
for example, are merely other grammatical expressions for aliquis 
or quidam. So Nonnihil, Nonnunquam, Nonnusquam, &c. 

The Latin tongue is almost peculiar among languages for such 
double negatives to express an affirmative. Of course the few 
which have found their place in Logic, instead of being despised 
or relegated to Grammar, have been fondly commented on by the 
ingenuity of the scholastic logicians. In English, some authors 
are fond of this indirect and idle way of speaking ; they prefer 
saying — "I entertain a not unfavourable opinion of such a one," 
to saying directly, I entertain of him a favourable opinion. 
Neglecting this, I pass on to 

The third species of Immediate Inference, noticed by the 
logicians. This they call Subalternation, but it may be more 
unambiguously styled Restriction. If I have £100 at my credit 
in the bank, it is evident that I may draw for £5 or £10. In like 
manner, if I can say unexclusively, that all men are animals, I can 
say restrictively, that negroes or any other fraction of mankind are 
animals. This restriction is Bilateral, when we restrict both sub- 
ject and predicate, as — 

All Triangle is all trilateral. All rational is all risible. 

.: Some triangle is some trilateral. .: Some rational is some risible. 

It is Unilateral, by restricting the omnitude or universality either 
of the Subject or of the Predicate. 
Of the Subject— 

All man is some animal; 
.'. Some man is some animal. 

Of the Predicate, as — 



268 APPENDIX. 

Some animal is all risible 
,: Some animal is some risible. 

It has not been noticed by the logicians, that there is only an 
inference by this process, if tlie some in the inferred proposition 
means some at least, that is, some not exclusive of all; for if we 
think by the some, some only, that is, some, not all, so far from 
there being any competent inference, there is in fact a real opposi- 
tion. The logicians, therefore, to vindicate their doctrine of the 
Opposition of Subalternation, ought to have declared, that the some 
was here in the sense of some only ; and to vindicate their doctrine 
of the Inference of Subalternation, they ought, in like manner, to 
have declared, that the some was here taken in the counter sense 
of some at least. It could easily be shown, that the errors of the 
logicians in regard to Oj)position, are not to be attributed to 
Aristotle. 

Before leaving this process, it may be proper to observe that we 
might well call its two propositions together the restringent or 
restrictive, {lyrojwsitiones 7'estringentes vel restrictivce) ; the given 
proposition might be called the restringend, (propositio restrin- 
genda), and the product the 7'estrict or restricted, {propositio 
restricta.) 

So much for the species of Immediate Inference recognised by 
the logicians. 

There is, however, a kind of immediate inference overlooked by 
logical writers. I have formerly noticed, that they enumerate, 
(among the species of Opposition), Suhcontrariety, (subcontrarietas, 
VTrevavTLOTT]'!;), to wit, — some is, some is not ; but that this is not 
in fact an opposition at all, (as in truth neither is Subalterna- 
tion in a certain sense.) Suhcontrariety, in like manner, is with 
them not an opposition between two partial somes, but between 
different and different ; in fact, no opposition at all. But if they 
are thus all wrong by commission, they are doubly wrong by 
omission, for they overlook the immediate inference which the 
relation of propositions in Suhcontrariety affords. This, however, 
is sufficiently manifest. If I can say, All men are some animals, 
or, Some animals are all men, I am thereby entitled to say, — 
All men are not some animals, or Some animals are not some 
men. Of course here the some in the inferred propositions means 



APPENDIX. 269 

some other, as in the original proposition, some only ; but the 
inference is perfectly legitimate, being merely a necessary explica- 
tion of the thought : for inasmuch as I think and say that all men 
are some animals, I can think and say that they are some animals 
only, which implies that they are a certain some, and not any 
other animals." This inference is thus not only to some others 
indefinitely, but to all others definitely. It is further either afiirma- 
tive from a negative antecedent, or negative from an aflirmative. 
rinally, it is not bilateral, as not of subject and predicate at 
once ; but it is unilateral, either of the subject or of the predi- 
cate. This inference of Subcontrariety, I would call Integration, 
because the mind here tends to determine all the parts of a whole, 
whereof a part only has been given. The two propositions toge- 
ther might be called the integral or integrant, {propositiones 
integrales vel integrantes). The given proposition would be styled 
the integrand, {'propositio integranda) ; and the product, tlie 
integrate, {propositio integrata). p 

I may refer you for various observations on the Quantification 
of the Predicate, to the collection published under the title, 
Discussions on Philosophy and Literature. 



The grand general or dominant result of the doctrine on which 
I have already partially touched, but which I will now explain 
consecutively and more in detail, is as follows : — Touching Proposi- 
tions, — Subject and Predicate ; — touching Syllogisms, — in Catego- 
ricals, Major and Minor Terms, Major and Minor Premises, Figures 
First, Second, Third, Fourth, and even what I call ISfo Figure, are 
all made convertible with each other, and all conversion reduced to a 
simple equation ; whilst in Hypotheticals, both the species, (viz. 
Conjunctive and Disjunctive reasonings), are shown to be forms 

a If we say some animal is all man, Therefore, some animals are not some 

and some animal is not amy man; in that animals. 

case, we must hold some as meaning fi Mem. Immediate inference of Con- 

some only. We may have a mediate tradictiou omitted. Also of Relation, 

syllogism on it, as : which would come under Equipollence. 

[For Tabular Schemes of Propositional 

Some animals are all men ; Forms, and of their Mutual Relations, 

Some animals are not any man; see below, i>p. 277, 278. — Ed.] 



270 APPENDIX. 

not of mediate argumentation at all, but merely complex varieties 
of the immediate inference of Eestriction or Subalternation, and 
are relieved of a load of perversions, limitations, exceptions, and 
rules. The differences of Quantity and Quality, &c. thus alone 
remain ; and by these exclusively are Terms, Propositions, and 
Syllogisms formally distinguished. Quantity and Quality combined 
constitute the only real discrimination of Syllogistic Mood. Syllo- 
gistic Figure vanishes, with its perplexing apparatus of special 
rules ; and even the General Laws of Syllogism proper are reduced 
to a single compendious canon. 

This doctrine is founded on the postulate of Logic : — To state 
in language, what is efficient in thought ; in other words, Before 
proceeding to deal logically with any proposition or syllogism, we 
must be allowed to determine and express what it means. 

First, then, in regard to Propositions. — In a proposition, the 
two terms, the Subject and Predicate, have each their quantity in 
thought. This quantity is not always expressed in language, for 
language tends always to abbreviation ; but it is always under- 
stood. For example, in the proposition, Men are animals, what 
do we mean? We do not mean that scyne men, to the exclusion 
of others, are animals, but we use the abbreviated expression 
inen for the thought all men. Logic, therefore, in virtue of 
its postulate, warrants, nay requires, us to state this explicitly. 
Let us, therefore, overtly quantify the subject, and say, All men 
are animals. So far we have dealt with the proposition, — 
we have quantified in language the subject, as it was quantified 
in thought. 

But the predicate still remains. We have said — A U men are 
animals. But what do we mean by animals ? Do we mean all 
animals, or some animals ? Not the former ; for dogs, horses, 
oxen, &c. are animals as well as men, and dogs, horses, oxen, &c. 
are not men. Men, therefore, are animals, but exclusively of dogs, 
horses, oxen, &c. All men, therefore, are not equivalent to all 
animals ; that is, we cannot say, as we cannot think, that all men 
are all animals. But we can say, for in thought we do affirm, 
that all men are some animals. 

But if we can say, as we do think, that all men are some 
anim.als, we can, on the other hand, likewise say, as we do think, 
that some animals are all m,en. 



APPENDIX. 271 

If this be true, it is a matter of indifference, in a logical point 
of view, (whatever it may be in a rhetorical), which of the two 
terms be made the subject or predicate of the proposition ; and 
whichsoever term is made the subject in the first instance, may, 
in the second, be converted into the predicate, and whichsoever 
term is made the predicate in the first instance, may, in the 
second, be converted into the subject. 

From this it follows : — 

1°, That a proposition is. simply an eqnation, an identification, 
a bringing into congruence, of two notions in respect to their 
Extension. I say, in respect to their Extension, for it is this quan- 
tity alone which admits of ampliation or restriction, the Compre- 
hension of a notion remaining always the same, being always taken 
at its amount. 

2°, The total quantity of the proposition to be converted, and 
the total quantity of the jiroposition the product of the conver- 
sion, is always one and the same. In this unexclusive point of 
view, all conversion is merely simple convei-sion ; and the dis- 
tinction of a conversion, as it is called, by accident, arises only 
from the partial view of the logicians, who have looked merely to 
the quantity of the subject. They, accordingly, denominated a pro- 
position universal or particular, as its subject merely was quanti- 
fied by the predesignation some or all ; and where a proposition 
like, All men are animals, (in thought, some animals), was con- 
verted into the proposition, Some animals are men, (in thought, 
all men), they erroneously supposed that it lost quantity, was re- 
stricted, and became a particular proposition. 

It can hardly be said that the logicians contemplated the re- 
conversion of such a proposition as the preceding ; for they did 
not (or rarely) give the name of conversio 'per accidens to the case 
in which the proposition, on their theory, was turned from a par- 
ticular into a universal, as when we reconvert the proposition. 
Some animals are men, into the proposition. All men are ani- 
mals.^ They lili:ewise neglected such affirmative propositions as 

o See above, vol. i. p. 264. — Ed. [A lius, Logica, t. ii. 1. i. q. i. c. 2, p. 32. For 

mistake by logicians in general, that Aristotle xises the terms universal, and 

partial conversion, eV /uepei, is the mere partial conversion, simply to express 

synonym of x>er accidens, and that the whether the convertens is an universal or 

former is so used by Aristotle. See Val- particular proposition. See § 4 of the 



272 ArPENDIX, 

had ill thought both subject and predicate quantified to their 
whole extent ; as, All triangular figure is trilate7xd, that is, if 
expressed as understood, All triangular is all trilateral figure, — 
All rational is risible, that is, if explicitly enounced, All rational 
is all risible animal. Aristotle, and subsequent logicians, had 
indeed frequently to do with propositions in which the predicate 
was taken in its full extension. In these the logicians, — but, be it 
observed, not Aristotle, — attempted to remedy the imjjerfection of 
the Aristotelic doctrine, which did not allow the quantification of 
the predicate to be taken logically or formally into account in 
affirmative propositions, by asserting that in the obnoxious cases 
the predicate was distributed, that is, fully quantified, in virtue of 
the matter, and not in virtue of the form, (vi materiw, non ratione 
formce). But this is altogether erroneous. Por in thought we 
generally do, nay, often must, fully quantify the predicate. In our 
logical conversion, in fact, of a proposition like All men are 
aniinals, — some animals, we must formally retain in thought, 
for we cannot formally abolish, the universal quantification of 
the predicate. We, accordingly, must formally allow the propo- 
sition thus obtained, — Some animals are all m.en. 

The error of the logicians is further shown by our most naked 
logical notation ; for it is quite as easy and quite as natural to 
quantify A, B, or C, as predicate, as to quantify A, B, or C, as 
subject. Thus, All^ is some A ; So7ne A is all B. 




A, -.B 



I may here also animadvert on the counter defect, the counter 

chapter on Conversion, {An. Prior., i. 2), ]ess,orfrom less to greater,s«?r« reritate, 

■\\ here particuhir affirmatives are said to the quality of the terms and projiosi- 

be necessarily converted, iv fiepei. tions remaining always the same. So 

Conversio ^5fr accidcvs is in two forms Ridiger, Z>e Sensu Veri et Falsi, p. 303. 

differently defined by different logicians. The second is that of logicians in gene- 

The first by Boethius, by whom the name ral, where the quantity of the proposi- 

was originally given, is that in which the tion is diminished, the quality of the 

quantity of the proposition is contin- propositions and terms rem.aiuing the 

gently changed either from greater to same, salva reritate.] 



APPENDIX. 273 

error, of the logicians, in their doctrine of Negative Propositions. 
In negative propositions they say the predicate is always distri- 
buted, — always taken in its full extension. Now this is altogether 
untenable. For we always can, and frequently do, think the pre- 
dicate of negative propositions as only partially excluded from the 
sphere of the subject. For example, we can think, as our naked 
diagrams can show, — All men are not some ammals, that is, not 
irrational animals. In point of fact, so often as we think a sub- 
ject as partially included within the sphere of a predicate, eo ipso 
we think it as partially, that is, jjarticularly, excluded therefrom. 
Logicians are, therefore, altogether at fault in their doctrine, that 
the predicate is always distributed, i.e. always universal, in negative 
propositions. " 

But, 3°, If the preceding theory be true, — if it be true that sub- 
ject and predicate are, as quantified, always simply convertible, 
the proposition being in fact only an enouncement of their equa- 
tion, it follows, (and this also is an adequate test), that we may at 
will identify the two terms by maldng them both the subject or 
both the predicate of the same proposition. And this we can do. 
For we can not only say — as A is B, so conversely B is A, or as 
All 7716)1 are some animals, so, conversely, Some animals are all 
men; but equally say — A and^ are convertible, or. Convertible 
are B and A; All men and some animals are convertible, (that is, 

a [Melanchthou, (Erotemata, L. li. Be both subject and predicate, in other 
Conversione, p. 516), followed by his words, to the whole proposition, 
pupil and commentator Strigelius, {In This doctrine is altogether erroneous. 
Erotemata, pp. 576, 581), and by Keck- It is an erroneous theory devised to 
ermann, {Syst. Log. Minus, L. ii. c. 3, Op. explain an erroneous pi'actice. In the 
p. 222), and others, thinks that " there first place, we have here a commutation 
is a greater force of the particle none, of negation with quantification ; and, at 
{nullus, not any), thunoi the Tpa^rticle all, the same time, conversion, direct con- 
{omnis). For, in a universal negative, version at least, will not be said to 
the force of the negation is so spread change the quality either of a negative 
over the whole proposition, that in its or affirmative proposition. In the se- 
conversion the same sign is retained, (as cond place, it cannot be pretended that 
— No star is consumed; therefore, no negation has an exclusive or even greater 
fiame ivhich is consumed is a star) : affinity to \iniversal than to particu- 
whereas such conversion does not take lar quantification. We can equally well 
place in a univei-sal affirmative." This say not some, not all, not any; and the 
Strigelius compares to the diffusion of reason why one of these forms is pre- 
a ferment or acute poison ; adding that ferred, lies certainly not iu any attrac- 
the affirmative particle is limited to the tion or aflSnity to the negative par- 
subject, whilst the negative extends to tide.] 

VOL. TI. S 



274 



APPENDIX. 



some convertible things), or, Convertible, (that is, some convertible 
things), are some animals and all men. By convertible, I mean 
the same, the identical, the congruent, &c.a 



The general errors in regard to Conversion, — the errors from 
which all the rest proceed, are — 

1°, The omission to quantify the predicate throughout. 

2°, The conceit that the quantities did not belong to the terms. 

3°, The conceit that the quantities were not to be transposed 
with their relative terms. 

4°, The one-sided view that the proposition was not equally 
composed of the two terms, but was more dependent on the sub- 
ject than on the predicate. 

0°, The consequent error that the quantity of the subject term 
determines the quantity of the proposition absolutely. 



a [With tbe doctrine of Conversion 
taught in the text, compare the follow- 
ing authorities ; — ■ Laurentius Valla, 
Dialectica, L. ii. c. 24, f. 37. Titius, 
Ars Cogitandi, (v. Ridiger, De Sensu 
Veri et Falsi, L. ii. c. i. p. 232). 
Reusch, Systema Logknm, § 380, p. 413 
et seq., ed. 1741. Hollmanu, Lorjica, § 89, 
p. 172. Ploucquet. Fries, Logik, § 33, 
p. 146. E. Reinhold, Looik, § 117, p. 
286, Ancients referred to by Am- 
monius, In De InUrp., c. vii., § 4, f. . . . 
Paulus Vallius, Logica, t. ii., In An. 
Prior., L. i. q. ii. c. iv.] [Valla I. c. 
says : — " Non amplius ac latins aceipitur 
prtedicatum quam subjectum. Ideoque 
cum illo converti potest, ut omnis homo 
est animal: non utique totum genus 
animal, sed aliqua pars hujus generis . . 
ergo, Aliqua pars animalis est in omni 
homine. Item, Quidam homo est ani- 
mal, scilicet est qucedam pars animalis, 
ergo, Qucedam pars animalis est qtiidam 
homo, &c." Gottlieb Gerhard Titius, 
Ars Cogitandi, c. vii. § 3 c< seq., p. 125. 
Lipsise, 1723 (first ed. 1701). " Nihil 
autem aliud agit Conversio, quam ut 
simpliciter pra3dicatum et subjectum 
transponat, hinc nee qualitatem nee 



quantitatem iis largitur, aut eas mutat, 
sed prout reperit, ita convertit. Ex 
quo necessario sequitur conversionem 
esse uniformem ac omnes propositiones 
eodem plane mode converti. Per ex- 
empla, (1), Nullus homo est lapis, ergo, 
Nullus laptis est homo, (2), Quidam homo 
non est medicus (omnis), ergo, Medicus 
non est homo quidam, seu Nullus medicus 
est homo quidam . . . (3), Hie Petrxos 
non est doctus (omnis), ergo, Omnis doc- 
tus nonesthic Petrus . . . (4), Omnis 
homo est animal (quoddam), ergo. Quod- 
dam animal est homo (5), Quidam homo 
currit (particulariter), ergo, Quidam cur- 
rens est homo, (6), Hie Paulus est docttis 
(quidam), ergo, Quidam doctus est hie 
Paulus. In omnibus his exemplis sub- 
jectum cum sua quantitate in locum 
praadicati, et hoc, eodem modo, in illius 
sedem transponitur, ut nulla penitus 
ratio solida appareat, quare conversi- 
onem in diversas species divellere de- 
beamus. Vulgo tamen aliter sentiunt 
quando triplicem conversionem, nempe 
simplicem, per accidens, ac pjer eontra- 
p)ositionem, adstruunt. . , . Enimvero 
conversio per accidens et per contraposi- 
tionem gratis asseritur, nam conversio 



APPENDIX. 



275 



(j°, The consequent error that there was any increase or dimi- 
nution of the total quantity of the proposition. 

7°, That thoroughgoing conversion could not take place by one, 
and that the simple, form. 

8°, That all called in at least the form of Accidental Conversion ; 
all admitting at the same time that certain moods remain incon- 
vertible. 

9°, That the majority of logicians resorted to Contraposition, 
(which is not a conversion at all) ; some of them, however, as 
Burgersdyk, admitting that certain moods still remained obstinately 
inconvertible. 

10°, That they thus introduced a form which was at best indi- 
rect, vague, and useless, in fact not a conversion at all. 

1 ] °, That even admitting that all the moods were convertible 
by one or other of the three forms, the same mood was convertible 
by more than one. 



propositionis aiBrmantis viniversalis per- 
inde simplex est ac ea qua universalis 
negans convertitur, licet post earn sub- 
j actum sit particulare ; conversionis 
enim hie nulla culpa est, qute quanti- 
tatem, quae non adest, largiri nee potest 
nee debet. . . . Error vulgaris doctrinaj, 
nisi fallor, inde est, quod esistimaverint 
ad conversionem simplicem requiri, ut 
pradicatum assumat signuni et quantita- 
tem subjecti . . . Conversionem ^:)er 
contrapositionem quod attinet, facile os- 
tendi potest (1) exempla heic jactari 
solita, posse converti simf)liciter ; (2) 
conversionem per contrapositionem, re- 
vera non esse conversionem ; intei'im (3) 
putativam istam conversionem non in 
universali afBrmante, et particulari ne- 
gante solum, sed in omnibus potius pro- 
positionibus locum habere . , . e.g., 
Quoddam animal non est quadrupes, ergo, 
Nidlus quadrupes est animal quoddam." 
See the criticism of the doctrine of 
Titius by Ridiger, quoted below, p. 311. 
Ploucquet, Methodus Calculandi in 
Logicis, p. 49 (1763). " Intellectio identi- 
tatis subjecti et preedicati est aj[jirmatio. 
• . . Omnis circulus est linea curva. 
Qua) propositio logice expressa ha^c est : 
— Omnis circulus est qvcedam linea curva. 



Quo pacto id, quod intelligitur in prsedi- 
cato identificatur cum eo quod intelligitur 
in subjecto. Sive norim, sive non norim 
prseter circulum dari quoque alias cur- 
varum species, verum tamen est quan- 
dam lineam curvam sensu comprehensivo 
sumtam, esse omnem circulum, seu om- 
nem circulum esse quandam lineam cur- 
vam." Vallius, I. c. " Negatives vero 
convertuntur et in j^articulares et in 
universales negativas ; ut si dicamus, 
Socrates non est lapis, convertens illius 
erit, Aliquis lapis non est Socrates, et 
Nullus lapis est Soa'ates, et idem di- 
cendum erit de omui alia simili proposi- 
tione." — Ed.] 

[That Universal Affirmative Proposi- 
tions may be converted simply, if their 
pi-edicates are reciprocating, see Cor- 
vinus, Instit. Phil. Rat., § 514. lense, 
1742. Baumgarten, Logica, § 280, 
1765. Scotus, In. An. Pr., L. i. qu. 
14. Ulrich, Instit. Log. et Met., 
§ i. 2, 177, (1785). Kreil, LogiJc, §§ 46, 
62, (1789). Isendoorn, Logica Peripa- 
tctica, L. iii. c. 8, pp. 430, 431. Wal- 
lis, Logica, L. ii. c. 7. Zabarella, In. 
An. Prior. Tahulce, p. 148. Lambert, 
Be Universaliori Calculi Idea, § 24 et 
seq:\ 



276 APPENDIX. 

1 2', That all this mass of error and confusion was from their 
overlooking the necessity of one simple and direct mode of con- 
version : missing the one straight road. 



We have shown that a judgment (or proposition) is only a 
comparison resulting in a congruence, an equation, or non-equa- 
tion of two notions in the quantity of Extension ; and that these 
compared notions may stand to each other, as the one subject and 
the other predicate, as both the subject, or as both the predicate of 
the judgment. If this be true, the transposition of the terms of 
a projDOsition sinks in a very easy and a very simple process ; 
whilst the whole doctrine of logical Conversion is superseded as 
operose and imperfect, as useless and erroneous. The systems, new 
and old, must stand or fall with their doctrines of the Conversion 
of propositions. 

Thus, according to the doctrine of the logicians, conversion 
applies only to the naked terms themselves: — the subject and 
predicate of the prejacent interchange places, but the quantity 
by which each was therein affected is excluded from the move- 
ment ; remaining to affect its correlative in the subjacent proposi- 
tion. This is altogether erroneous. In conversion we transpose 
the compared notions, — the correlated terms. If we do not, ever- 
81071, not conversion, is the result. 



If, (as the Logicians suppose), in the convertens the subject 
and predicate took each other's quantity, the proposition would 
be not the same relation of the same notions. It makes no 
difference that the converse only takes place when the subject 
chances to have an equal amount or a less than the predicate. 
There must be at any rate a reasoning, (concealed indeed), to 
warrant it : in the former case — that the predicate is entitled to 
take all the quantity of the subject, being itself of equivalent 
amount ; in the second, (a reasoning of subalternation), that it is 
entitled to take the quantity of the subject, being less tlian its 
own. All this is false. Subject and predicate have a right to 
their own, and only to their own, which they carry with them, 
when they become each other. 



APPENDIX. 



:// 



{d) APPLICATION OF DOCTRINE OF QUANTIFIED 
PREDICATE TO PROPOSITIONS. 

(1). New Pkopositional Forms — Notation. 

Instead of four species of Proposition determined by the Quantity 
and Quality taken together, the Quantity of the Subject being 
alone considered, there are double that number, the Quantity of the 
Predicate being; also taken into account. 




(2B 



Affirmative. 
(1) [AfA] C: 
(ii) [Afl] C:: 

(3) [If A] A,^ 
(iv) [If I] 0,: 

Negative, 
(v) [EnE] 
( A) (A) 
(6) [EnO] C: 

(A) (I) 
(vii) [OnE] B, 

(I) (A) 
(8) [OnO] C, 

(I) (I) 



- : r All Triangle is all Trilateral [fig. 1]. 
-, A AU Triangle is some Figure (A) 

[fig- 2]. 
- : C Some Figure is all Triangle [fig. 2]. 
-•, B Some Triangle is some Equilateral 

(I) [fig. 4]. 

: D Any Triangle is not any Square (E) 

- , B Any Triangle is not some Equilateral 

[fig. 4]. 
- : C Some Equilateral is not any Triangle 

(0) [fig. 4]. 

- ,B Some Triangle is not some Equila- 

teral [fig. 4].« 



« [In this table the Roman numerals 
(listingnish such prepositional forms as 
are recognised in the Aristotelic or 
common doctrine, whereas the Arabic 
ciphers mark those (half of the whole) 
which I think ought likewise to be 
recognised. In the literal symbols, I 
simplify and disintricate the scholastic 
notation ; taking A and I for universal 
and particular, but, extending them to 
either qualit}% marking affirmation by f, 
negation by n, the two first consonants 



of the verbs affirmo and nego, — verbs 
from which I have no doubt that Petnis 
Hispanus drew, respectively, the two first 
vowels, to denote his four complications 
of quantity and quality.] — Discussions, 
p. 686. 

[In the notation emjjloyed above, the 
comma , denotes some ; the colon : all ; 
the line »=— denotes the affirmative 
copula, and negation is expressed by 
drawing a line through the affirmative 
copula ia4~ J ^^s thick end of the line 



278 



APPENDIX. 



(2). Quantity of Propositions — Definitude and 
Indefinitude. 

Nothing can exceed the ambiguity, vacillation, and uncertainty 
of logicians concerning the Quantity of Propositions. 

I. As regards what are called indefinite (aStoptcrrot more pro- 
perly indesignate or preindesignate projwsitmis. The absence of 
overt quantification applies only to the subject ; for the predicate 
was supposed always in affirmatives to be particular, in negatives to 
be universal. Keferring, therefore, only to the indesignation of the 
subject : — indefinites were by some logicians, (as the Greek com- 
mentators on Aristotle (?), Apuleius aptid Waitz, In Org. i. p. 
338, but see Wegelin, In Aneponymi Phil. Syn., p. 588), made 
tantamount to particulars : by others, (as Valla, Dialectica, L. 
ii. c. 24, f. 37), made tantamount to imiversals. They ought 
to have been considered as merely elliptical, and to be definitely 
referable either to particulars or universals." 



denotes the subject, the thin end the 
predicate, of Extension. In Intension 
the thin end denotes the subject, the 
thick end the predicate. Thus : — 
C : i^— , A is read, All C is some A. 
C : H— : D is read, No C is any D. The 
Table given in the text is from a copy 
of an early scheme of the author's new 
Prepositional Forms. For some time 
after his discovery of the doctrine of a 
quantified predicate, Sir W. Hamilton 
seems to have used the vowels E and 
O in the formula) of Negative Proposi- 
tions ; and the full period (.) as the 
symbol of some (indefinite quantity). In 
the college session of 1845-46, he had 
adopted the comma (,) as the symbol of 
indefinite quantity. As the period ap- 
pears in the original copy of this table 
as the symbol of some, its date cannot 
be later than 1845. The comma (,) has 
been substituted by the Editors, to adapt 
the table to the Author's latest form of 
notation. The translation of its symbols 
into concrete propositions, affords deci- 
sive evidence of the meaning which the 
Author attached to them on the new 
doctrine. That this, moreover, was the 
tmiform import oi Sir W. Hamilton's 
prepositional notation, from the earliest 
development of the theoi-y of a quantified 



predicate, is placed beyond doubt by 
numerous passages in papei-s (not print- 
ed), and b}^ marginal notes on books, 
written at various periods between 1839- 
40, and the date of his illness, July 1844, 
when he was compelled to employ an 
amanuensis. The letters in round brack- 
ets, (A) and (I), are the vowels finally 
adopted by the Author, in place of E and 
0. See below, p. 283, Ed.] 

a [That Indefinite propositions are to 
be referred to universals, see Purchot, 
Instit. Phil. Lof/ica, I. § ii. c. 2, pp. 124, 
125, 126. Kottenbeccius, Logirn Con- 
tracta, c. vi. p. 92, (1560). Baumeister, 
Inst. Phil. Rat., § 213. J. C. Scaliger, 
Exercitationes, Ex. 212, § 2. Drobisch, 
Logik, § 39. Neomagus, Ad Traiiezun- 
tium, f. 10. To be referred to particular; 
see Lovanienses, Com. in Arist. Dial. p. 
161. MolinEeus, Elementa Logica, L. I. 
c. 2. Alex. Aphrod, In An. Prior., c. ii. 
p. 19. Denzinger, Logica, § 71. Either 
universal or particular, Keckermann, 
Opera, p. 220. Aristotle doubts : see 
An. Prior, L. I. c. 27, •§ 7, and Be 
Intcrp. c. 7. That Indefinitude is no 
separate species of quantity, see Schei- 
bler. Opera Logica, p. iii. c. 6, p. 443. 
Grgecus Anonymus, De Si/llogismo, L. 
i. c. 4, f. 42. Leibnitz, Opera, t. iv. 



APPENDIX. 279 

II. A remarkable uncertainty prevails in regard to the meaning 
of particularity and its signs, — some, &c. Here some may mean 
some only — some not all. Here some, though always in a certain 
degree indefinite, is definite so far as it excludes omnitude, — is used 
in opposition to all. This I would call its Semi-definite meaning. 
On the other hand, some may mean some at least, — some, perhaps 
all. In this signification some is thoroughly indefinite, as it does 
not exclude omnitude or totality. This meaning I would call the 
Indefinite. 

Now of these two meanings there is no doubt that Aristotle used 
particularity only in the second, or thoroughly Indefinite, meaning. 
For 1°, He does not recognise the incompossibility of the super- 
ordinate and subordinate. 2°, He makes all and ov Tra? or particu- 
lar negative, to be contradictories ; that is, one necessarily true, the 
other necessarily false. But this is not the case in the Semi-definite 
meaning. The same holds good in the Universal Negative, and 
Particular Affirmative. 

The particularity, — the some, — is held to be a definite soTne when 
the other term is Definite, as in ii and 3, in 6 and vii. On the 
other hand, when both terms are Indefinite or Particular, as in iv. 
and 8, the some of each is left wholly indefinite. 

The quantification of definitude or non-imrticidarity (:) may 
designate ambiguously or indifferently one or other of three con- 
cepts. 1°, It may designate explicit omnitude or totality ; which, 
when expressed articulately, may be denoted by (::). Thus — All 
tria7igles are all trilatei'als. 2°, It may designate a class con- 
sidered as undivided, though not positively thought as taken in its 
whole extent ; and this may be articulately denoted by (:.). Thus 
— The triangle is the trilateral ; — The dog is the lati'ant. — 
(Here note the use of the definite article in English, Greek, French, 
German," &c.) 3°, It may designate not what is merely undivided, 

p. iii. p. 123. Fries, System der Lof/ik, logical import, when we do not know 

§ 30, p. 137. Eamus, Schol. Dial., L. whether all, or some, of the one be to 

vii. c. 2, p. 457. Downam, Jn Rami be affirmed or denied of the other. E. 

Dialect., L. ii. c. 4, p. 359. Facciolati, Reinhold, Lo'jik, § 88. Anm. 2, pp. 193, 

Rud. Log. p. ii. c. iii., p. 67. Delari- 194. Ploucquet, Methodus Calcidandi, 

y'lhre, Nouvelle Logique Classique, h. ii. pp. 48, 53, ed. 1773. Lambert, Neues 

s. ii. c. 3, s. 580, p. 334. Organon, I., § 235, p. 143.] 

That Indefinitude has sometimes a a [On effect of the definite article and 



280 



APPENDIX. 



though divisible, — a class, but what is indivisible, — an individual ; 
and this may be marked by the small letter or by (:) — Thus 
— Socrates is the hushand of Xanthijipe ; — This horse is 
Bucephalus. 

In like manner particularity or indefinitude (,), when we wish 
to mark it as thoroughly indefinite, may be designated by (',), 
whereas when we would mark it as definitely indefinite, as ex- 
cluding all or not any, may be marked by ("). 

The indefinites (aopiara) of Aristotle correspond sometimes to 
the particular, sometimes to one or other, of the two kinds of 
universals." 



The designation of indefinitude or partictdarit>/, some (, or ,) 
may mean one or other of two very different things. 

1°, It may mean some and some only, being neither all nor none, 
and, in this sense, it will be both affirmative and negative, (,,). 

2°, It may mean, negatively, not all, perhaps none, some at 
most; affirmatively, 7iO^ none, perhaps all, — some at least, (, ,). 

Aristotle and the logicians contemplate only the second mean- 



its absence in different languages, in re- 
ducing the definite to tlie indefinite, 
see Delariviere, Logique, §§ 580, 581. 

On the Greek article, see Ammonivis, 
In De Interp. c. vii. f. 67 b. 

On use of the Arabic article in quan- 
tification, see Averroes, De Interp., p. 
39, ed. 1552 :— 

" Al in the Arabic tongue, and Ha 
in the Hebrew, and in like manner the 
articles in other languages, sometimes 
have the power of universal predesigna- 
tions, sometimes of particular. If the 
former, then they have the force of con- 
traries ; if the latter, then the force of 
sub-contraries. For it is true to say, al, 
that is, /^3se Jiomo is white, and al, that 
is, ijjse homo is 7iot white ; that is, when 
the article al or ha, that is, ipse, denotes 
the designation of particularity. They 
may, however, be at once false, when 
the article al or ha has the force of the 
universal predesignation." (See also p. 
52 of the same book.) 

In English the definite article always 
defines, — renders definite, — but some- 
times individualises, and sometimes ge- 



neralises. If we would use man gene- 
rally, we must not prefix the article, as 
in Greek, German, French, &c., so wealth, 
government, &c. But in definition of 
horse. Sec, the reverse, as the dog, (le 
chien, 6 kvuv, &c.) A in English is often 
equivalent to anyP\ 

a [Logicians who have marked the 
Quantities by Definite, Indefirate, &c. 

Aristotle, A)i. Pr. c. iv. § 21, and 
thei'e Alexander, Pacius. Theophras- 
tus, (Facciolati, Riid. Log., p. i. c. 4, 
p. 39.) Ammonius, In De Inter., f. 72 b. 
(Brandis, Scholia, p. 113.) Stoics and 
Non-peripatetic Logicians in general, 
see Sext. Empiricus, Adv. Log., § 98 
ef seq., p. 476, ed. Fabricii ; Diog. 
Laert. Lib. vii. seq. 71, ubi Menagius. 
Dowuam, In Hami Dialecticam, L. ii. 
c. 4, p. 363, notices that a parti- 
cular proposition " was called by the 
Stoics indefinite, {aipiffrov) ; by some 
Latins, and sometimes by Ramus him- 
self, infinite; because it does not de- 
signate some certain species, but leaves 
it uncertain and indefinite." Hurtado de 
Mendoza, Dis^). Log. et Met., t. i. d. iv. § 



APPENDIX. 281 

ing. The reason of this perhaps is, that this distinction only 
emerges in the consideration of Opposition and Immediate Infer- 
ence, which were less elaborated in the former theories of Logic ; 
and does not obtrude itself in the consideration of Mediate Infer- 
ence, which is there principally developed. On the doctrine of the 
logicians, there is no opposition of snbalternation ; and by Aris- 
totle no opposition of snbalternation is mentioned. By other 
logicians it was erroneously introduced. The opposition of Sub- 
contraries is, likewise, improper, being precarious and not between 
the same things. Aristotle, though he emmierates this opposition, 
was quite aware of its impropriety, and declares it to be merely 
verbal, not real." 

By the introduction of the first meaning of some, we obtain a 
veritable opposition in Snbalternation ; and an inference in Sub- 
contrariety, which I would call Integration. 

(3.) Opposition of Peoposittons. 

Propositions may be considered under two views ; according as 
their particularity, or indefinitude, is supposed to be thoroughly 
indefinite, unexclusive even of the definite ; some, meaning some 
at least, some, perhaps all, some, perhaps not any ; or definite 
indefinitude, and so exclusive of the definite ; some, meaning some 
at most, — some only, — some not all, &c. The latter thus excludes 
omnitude or totality, positive or negative ; the former does not. 
The former is the view promulgated as alone contemplated by 
Aristotle ; and has been inherited from him by the Logicians, with- 
out thought of increase or of change. The latter is the view which 
I would introduce ; and though it may not supersede, ought, I 
think, to have been placed alongside of the other. 

Causes of the introduction of the Aristotelic system alone : — 
1°, To allow a harmony of Logic with common language ; for 
language eliding all that is not of immediate interest, and the 
determination of the subject-notion being generally that alone 
intended, the predicate is only considered in so far as it is thought 
to cover the subject, that is, to be at least co-extensive with it. 

2, p. 114. 'LoY&menaes,, In Arist. Dial., \>. a On both forms of Opposition, see 

161. Hollmann,Zo^/ca,p. 173. Boethius, Scheibler, [Oi^cra Logica, § iii., de Pro- 

Ojjera, p. 345. Rensch, St/st. Log., -p. i2i. positionibus, c. xi. p. 487, and above, 

Esser, LogiJc, § 58. Weiss, Logik, §§ 149, vol. i. p. 261.— Ed.] 
150. So Kiesewetter, Logik, §§ 102, 103.] 



282 APPENDIX. 

But if we should convert the terms, the inadequacy would be 
brouoht to li2;]it. 

2°, A great number of notions are used principally, if not ex- 
clusively, as attributes, and not as subjects. Men are, consequently, 
very commonly ignorant of the proportion of the extension be- 
tween the subjects and predicates, which they are in the habit of 
combining into propositions. 

3°, In regard to negatives, men naturally preferred to attribute 
positively a part of one notion to another than to deny a part. 
Hence the unfrequency of negatives with a particular predicate. 

On the doctrine of Semi-definite Particularity, I would thus 
evolve the Opposition or Incompossibility of propositions, neglect- 
ing or throwing aside (with Aristotle) those of Subalternation 
and Sub-contrariety, but introducing that oi Inconsistency. 

Incompossibility is either of propositions of the same, or of dif- 
ferent, quality. Incompossible propositions differing in quality are 
either Contradictories without a mean, — no third, — that is, if one be 
true the other must be false, and if one be false the other must be 
true ; or Contraries with a mean, — a third, — that is, both may be 
false, but both cannot be true. Incompossible propositions of the 
same quality are Inconsistents, and, like Contraries, they have a 
mean, that is, both may be false, but both cannot be true. 

Contradictories are again either simple or complex. The simple 
are either, 1", Of Universals, as undivided wholes; or, 2°, Of In- 
dividuals, as indivisible parts. « 

The complex are of universals divided, as 4 — 5. 

Contraries, again, which are only of divided universals, are 1°, 
Bilateral, as 1 — 5 ; or, 2°, Unilateral, as 1 — 6, 1 — 7, 2 — 5, 3 — 5 ; 
or, 3", Cross, as 2—7, 3—6. 

Inconsistents are either, 1°, Affirmatives ; or, 2°, Negatives. Af- 
firmatives, as 1 — 2, 1 — 3, 2 — 3. Negatives, as 5 — 6, 5 — 7. The pro- 
positions 6 — 7 are sometimes Inconsistents, sometimes Coosistents. 

All the other propositional forms, whether of the same or of 
different qualities, are Compossible or Unopposed. 

The differences in Compossibility of the two schemes of Indefin- 
ite and Definite particularity lies, 1°, in the whole Inconsistents ; 
2°, in two Contraries for Contradictories. 1°, According to the 

a General terms, used as individual Man is not mortal. So that there are 
terms, when opposed to each other, may three kinds of conti'adictories. 
be contradictories, as Man is mortal, 



APPENDIX. 283 

former, all affirmative and all negative propositions are consistent, 
whereas in the latter these are inconsistent, ] — 2, 1 — 8, 2 — 3 ; 
among the affirmatives, and among the negatives, 5 — 6, 5 — 7. 
(As said before, 6 — 7 is in both schemes sometimes compossible, 
and sometimes incompossible). 2°, Two incompossibles, to wit, 
2 — 7, 3 — 6, which, on the Aristotelic doctrine, are Contradictories, 
are in mine Contraries. 

The propositional form 4 is consistent with all the affirmatives ; 
8 is not only consistent with all the negatives, but is compossible 
with every other form in universals. It is useful only to divide a 
class, and is opposed only by the negation of divisibility. 

By adopting exclusively the Indefinite particularity, logicians 
threw away some important immediate inferences ; those, to wit, 1°, 
From the affirmation of one some to the negation of another, and 
vice versa; and, 2°, From the affirmation of one inconsistent to the 
negation of another. 1°, Thus, on our system, but not on theirs, 
affirming all man to he some animal, we have a right to infer that 
no man is some {other) animal; affirming that some animal is all 
man, we have a right to infer that some {other) animal is not any 
man ; affirming some men are some blacks, {Negroes), we are en- 
titled to say that {same) some men are not some {other ) blacks, 
{Hindoos), and also that {other) some men are not the {same) some 
blacks. And so backwards from negation to affirmation. This 
inference I would call that of [Integration]. 

2°, Affirming all men ai^e some animals, we are entitled to 
infer the denial of the propositions, all men are all animals, some 
men are all animals. And so in the negative inconsistents. 

Affieimatives. 

1.) Toto-total = Afa = All — is all — . 

ii.) Toto-partial = Afi = All — is some — . (A) 

3.) Parti-total = Ifa = Some — is all — . 

iv.) Parti-partial = Ifi = Some — is some — . (I) 

Negatives. 
V.) Toto-total — Ana = Any — is not any — . (E) 
6.) Toto-partial = Ani = Any — is not some — . 
vii.) Parti-total = Ina = Some — is not any — . (0) 
8.) Parti-partial = Ini = Some — is not some — . 



28 1 



APPENDIX. 



TABLE OF THE Mutual Relations of the Eight Propositional Forms 
ON Either System of Particularity. (For Generals only.) 



II. 

Inverence 

from Proposition to Proposition, ou the 

two Systems. 


2. 

Definite Indeflni- 

tude. 

(Some at most.) 


Restr. bi. 

Restr, un. 
Restr. un. 


Restr. bi. 

Restr. un. 
Restr. un. 


Res. & Int. bi. 
Integr. un. 
Res. & Int. un. 

Integr. un. 
Res. & Int. un. 

Res. & Int. un. 
Res. k Int. un. 
Integr. bi. 


1. 
Indefinite Defini- 

tude. 
(Some at least.) 


a d._; d a 

3 3,^2 3 3 


d d.A a d 

3 3rQ 3 3 




Restr 
Restr 
Restr 

Restr 
Restr 


Restr 
Restr 
Restr 

Restr 
Restr 


o 


1— ii 

1—3 
1— iv 

ii — iv 
3-iv 


V— 6 
V — vii 

V— 8 

6-8 
vii— 8 


1-8 
ii— 6 

ii-8 

3— vii 
3-8 

iv— 6, 6— iv 

iv — vii, vii — iv 

iv— 8, 8— iv 


I. 

Incompossibility 

of Proposition with Proposition, on 

the System of 


Definite Indefini- 

tude. 

(Some at most.) 


Incons. un. 
Incons. un. 

Incons. un. cr. 


Incons. un. 
Incons. un. 

Doubtful cr. 


Contrar. bi. 
Contrar. un. 
Contrar. un. 

Contrar. un. 

Contrar. bi. cr. 

Contrar. un. 
Contrar. bi. cr. 

Contrar. bi. di. 


1. 

Indefinite Defini- 

tude. 

(So7ne at least.) 




1 

o 

Q 


Contrar. bi. 
Contrar. un. 
Contrar. un. 

Contrar. un. 

Rejjugn. bi. cr. 

Contrar. un. 
Repugn, bi. cr. 

Repugn, bi. di. 


Common to I. and II., 

iu either of which 

all Propositions are related. 

Of these their 


"3 
> 


Mill! 


1 1 1 1 II 

rt c3 c3 ..-1 .1-1 _3 

a a a a a 2 
ol <- <j <J << »5 


M M 1 1 1 1 1 1 1 1 1 1 II 

:^:|:^:5^:^^:^;§^j|;|jajajaca 


-73 

'A 


Afl5rmat. 
1— ii 
1—3 
1-iv 
ii-3 
ii — iv 
3— iv 
Nea-at. 


•M .« ti ._ .^ .M :3 
'n'?CO'?GO0O^ >?o"?oo t»to'>ooioo'>oo t>«o >-Q0 

1 1 1 II r. 1 1 1 1 1 1 II 1 II 1 M 1 1 

> i> > CO to :a 5t) "-I "-I "-1 1-1 :S :a :a :a 50 CO CO CO >>,^> 



Abbreviations: — hi. = lilateral ; cr. =: cross ; Contrar. = Contraries; A\. = direct ; 
Incons. := Inconsistenis ; Int. or Integr. = Integration ; Repugn. = Repugnan.ts, Contra- 
dictories ; Res. or Restr. = Restriction, Suhalter nation ; un. = unilateral. — Blanks: in I. 
= Compossihles; in II. = No inference. — (Unilateral, bilateral, cross, direct, refer to the 
Extremes. ) 

The preceding Table may not be quite accurate in details. 



APPENDIX. 285 



(e) SYLLOGISMS. 

Observations on the Mutual Eelation of Syllogistic 
Terms in Quantity and Quality. 

General Canon. — What worst relation of subject and predicate, 
subsists between either of two terms and a common third term, 
with which one, at least, is positively related ; that relation 
subsists between the tiuo terms themselves. 

There are only three possible relations of Terms, (notions, repre- 
sentations, presentations). 

1°, The relation of Toto-total Coincliision, (coidentity, absolute 
convertibility or reciprocation) (AfA). 

2°, The relation of Toto-total Coexclusion, (non-identity, abso- 
lute inconvertibility or non-reciprocation) (An A). 

3°, The relation of Incomplete Coinclusion, which involves the 
counter-relation of Incomplete Coexclusion, (partial identity and 
non-identity, relative convertibility and non-convertibility, reci- 
procation, and non-reciprocation). This is of various orders and 
degrees. 

a) Where the whole of one term and the part of another are 
coinclusive or coidentical (Afl). This I call the relation of 
toto-partial coinclusion, as All rtien are some animals. This 
necessarily involves the counter-relation of toto-partial coexclu- 
sion (AnI), as Any man is not some animal. But the con- 
verse of this affirmative and negative affords the relations of 

b) Parti-total Coinclusion ( IfA), and Coexclusion (InA), as 
Somne animal is all man, Sonne anir)ial is not any man. 

c) There is still a third double relation under this head, when 
two terms partially include and partially exclude each other (If I 
Inl), as Some ivomen are some authors, and Some women are 
not some authors. This relation I call that of Parti-partial 
Coinclusion, and Parti-partial Coexclusion. 

Of these three general relations, the first is [technically styled] 
the best ; the second is the worst ; and the third is intermediate. 

Former logicians knew only of two worse relations, — a particular, 
worse than a universal, affirmative, and a negative worse than an 
affirmative. As to a better and worse in negatives, they knew 



286 



APPENDIX. 



nothing ; for as two negative premises were inadmissible, they had 

no occasion to determine which of two negatives was the worse or 

better. But in quantifying the predicate, in connecting positive 

and negative moods, and in generalising a one supreme canon of 

syllogism, we are compelled to look further, to consider the inverse 

procedures of affirmation and negation, and to show {e.g. in v. a. 

and vi. b., ix. a. and x. b), how the latter, by reversing the former, 

and turning the best quantity of affirmation into the worst of 

negation, annuls all restriction, and thus apparently varies the 

quantity of the conclusion. It thus becomes necessary to show 

the whole order of best and worst quantification throughout the 

two qualities, and how affirmation commences with the whole in 

Inclusion and Negation, with the parts in Exclusion. « 

Toto-total, ] 

Toto-partial, I , . 

-r, , . , , ) Identity or Comclusion. 

Parti-total, | "^ 

Parti-partial. / 
Parti-partial,^ 
Parti-total, I . 
Toto-partial, 




Non-identitvor Coexclusion. 



Toto-total. 

As the negation always reduces the best to the worst relation, 
in the intermediate relations determining only a commutation from 
equal to equal, whilst in both, the symbols of quantity, in their in- 
verse signification, remain externally the same ; it is evident, that 
the quantification of the conclusion will rarely be apparently diffe- 
rent in the negative, from what it is in the corresponding positive, 
mood. There are, indeed, only four differences to be found in the 
negative from the positive conclusions, and these all proceed on the 
same principle — viz. in v. a. and vi. b., in ix, a. and x. b. Here 
the particular quantification of the positive conclusions disappears 
in the negative moods. But this is in obedience to the general 
canon of syllogism, — " that the worst relation subsisting between 
either extreme and the middle, should subsist between the extremes 
themselves." For what was the best relation in the former, becomes 
the worst in the latter ; and as affirmation comes in from the 
greatest whole, whilst negation goes out from the least part, so, in 
point of fact, the some of the one may become the not any of the 



a See Magentinus, (in Brandis, Scholia, p. 113, and there the Platonics.) 



APPENDIX. 



287 



other. There is here, therefore, manifestly no exception. On the 
contrary this affords a striking example of the universal applicabi- 
lity of the canon under every change of circumstances. The canon 
would, in fact, have been invalidated, had the apparent anomaly 
not emero;ed. 



I. Terms each totally coinclu- 
sive of a third, are totally co- 
inclusive of each other. 



II. Terms each parti- totally 
coinclusive of a third, are parti- 
ally coinclusive of each other. 



III. A term totally, and a 
term parti-totally, coinclusive of 
a third, are toto-partially coin- 
clusive of each other. 



IV. A term parti-totally, and 
a term totally, coinclusive of a 
third, are j)arti-totally coinclu- 
sive of each other. 



V. A term totally, and a term 
toto-partially, coinclusive of a 



a) A term totally coexclu- 
sive, and a term totally coin- 
clusive, of a third, are totally 
eoexclusive of each other. 

b) A term totally coinclu- 
sive, and a term totally eoex- 
clusive, of a third, are totally 
eoexclusive of each other. 

a) A term parti-totally co- 
exclusive, and a term parti-totally 
coinclusive, of a third, are parti- 
ally eoexclusive of each other. 

b) A term parti-totally coin- 
clusive, and a term parti-totally 
eoexclusive, of a third, are par- 
tially eoexclusive of each other. 

a) A terra totally eoexclusive, 
and a term parti-totally coin- 
clusive, of a third, are toto-parti- 
ally eoexclusive of each other. 

b) A term totally coinclusive, 
and a term parti-totally eoexclu- 
sive, of a third, are toto-j)artially 
eoexclusive of each other. 

a) A term parti-totally co- 
exclusive, and a term totally co- 
inclusive, of a third, are joarti- 
totally eoexclusive of each other. 

b) A term parti-totally co- 
inclusive, and a term totally co- 
exclusive, of a third, are jjarti- 
totally eoexclusive of each other. 

a) A term totally eoexclusive, 
and a term toto-partially coin- 



288 



APPENDIX. 



third, are parti-totally coinclu- 
sive of each other. 



VI. A term toto - partially, 
and a term totally, coiiicliisive 
of a tliird, are toto -partially 
coiiiclusive of each other. 



VII. A term parti-totally, and 
a term partially, coinclusive of a 
third, are partially coinclusive 
of each other. 



VIII. A terra partially, and a 
term parti-totally, coinclusive of 
a third, are partially coinclusive 
of each other. 



IX. A term totally, and a 
term partially, coinclusive of a 
third, are partially coinclusive of 
each other. 



X. A term partially, and a 
term totally, coinclusive of a 



elusive, of a third, are totally 
coexclusive of each other. 

b) A term totally coinclusive, 
and a term toto-partially coex- 
clusive, of a third, are parti-totally 
coexclusive of each other. 

a) A term toto-partially co- 
exclusive, and a term totally co- 
inclusive, of a third, are toto-par- 
tially coexclusive of each other. 

b) A term toto-partially co- 
inclusive, and a term totally co- 
exclusive, of a third, are totally 
coexclusive of each other. 

a) A term parti-totally co- 
exclusive, and a term partially 
coinclusive, of a third, are parti- 
ally coexclusive of each other. 

b) A term parti-totally co- 
inclusive, and a term jjartially 
coexclusive, of a third, are par- 
tially coexclusive of each other. 

a) A term partially coexclu- 
sive, and a term parti-totally co- 
inclusive, of a third, are partially 
coexclusive of each other. 

b) A term partially coinclu- 
sive, and a term parti-totally co- 
exclusive, of a third, are partially 
coexclusive of each other. 

a) A term, totally coexclusive, 
and a term partially coinclusive, 
of a third, are parti-totally co- 
exclusive of each other. 

b) A term totally coinclusive, 
and a term jiartially, coexclusive 
of a third, are partially coexclu- 
sive of each other. 

a) A term partially coexclu- 
sive, and a term totally coinclu- 



APPENDIX. 



289 



third, are partially coiucliisive of 
each other. 



XI. A term parti-totally, and 
a term toto-partially, coinclusive 
of a third, are parti-totally co- 
inclusive of each other. 



XII. A term toto-partially, 
and a term parti-totally, coinclu- 
sive of a third, are toto-partially 
coinclusive of each other. 



sive of a third, are partially co- 
exclusive of each other. 

b) A term partially coinclu- 
sive, and a term totally coexclu- 
sive, of a thii'd, are toto-partially 
coexclusive of each other. 

a) A term parti-totally coex- 
clusive, and a term toto-parti- 
ally coinclusive, of a third, are 
parti-totally coexclusive of each 
other. 

b) A term parti-totally coin- 
clusive, and a term toto-partially 
coexclusive, of a third, are parti- 
totaUy coexclusive of each other. 

a) A term toto-partially coex- 
clusive, and a term parti-totally 
coinclusive, of a third, are toto- 
partiaUy coexclusive of each 
other. 

b) A term toto-partially co- 
inclusive, and a term parti-totally 
coexclusive, of a third, are toto- 
partially coexclusive of each 
other. 



(y).__OBJECTIONS TO THE DOCTRINE OF A QUANTIFIED 
PREDICATE CONSIDERED. 

(I). Geneeal. 



MATERIAL AND FOEMAL.— THEIR DISTINCTION. 

But it is requisite, seeing that there are such misconceptions 
prevalent on the point, to determine precisely, what is the formal 
which lies within the jurisdiction of Logic, and which Logic gua- 
rantees, and what the material which lies without the domain of 
Logic, and for which Logic is not responsible. This is fortunately 
easy. 

VOL. II. T 



290 APPENDIX. 

Logic knows, — takes cognisance of, certain general relations ; 
and from these it infers certain others. These and these alone it 
knows and guarantees ; and these are formal. Of all beyond these 
forms or general relations it takes no cognisance, affords no assur- 
ance ; and only hypotlietically says, — If the several notions applied 
to these forms stand to each other in the relation of these forms, 
then so and so is the result. But whether these notions are rightly 
applied, that is, do or do not bear a certain reciprocal dependence, 
of this Logic, as Logic, knows nothing. Let ABC represent three 
notions, A containing B, and B containino; C ; in that case Logic 
assures us that C is a part of B, and B a part of A ; that A contains 
C ; that C is a part of B and A. Now all is formal, the letter: 
being supposed to be mere abstract symbols. But if we apply to 
them, — fill them up by, — the three determinate notions,— iL?u'maZ 
— 3Ian — Negro, we introduce a certain "inatter, of which Logic is 
not itself cognisant ; Logic, therefore, merely says, — If these notions 
hold to each other the relations represented by A B C, then the 
same results will follow ; but whether they do mutually hold these 
relations, — that, as material, is extra-logical. Logic is, therefore, 
bound to exhibit a scheme of the forms, that is, of the relations in 
their immediate and mediate results, which are determined by the 
mere necessities of thinking, — by the laws of thought as thought ; 
but it is bound to nought beyond this. That, as material, is beyond 
its jurisdiction. However manifest, this has, however, been fre- 
quently misunderstood, and the material has been currently passed 
off in Logic as the formal. 

But further. Logic is bound to exhibit this scheme full and un- 
exclusive. To loj) or limit this in conformity to any circumstance 
extrinsic to the bare conditions, — the mere form, of thought, is a 
material, and, consequently, an illegitimate curtailment. To take, 
for instance, the aberrations of common language as a model, 
would be at once absurd in itself, and absurd as inconsistent even 
with its own practice. And yet this double absurdity the Logic 
now realised actually commits. For while in principle it avows 
its allegiance to thought alone ; and in part it has overtly repudi- 
ated the elisions of language ; in part it has accommodated itself 
to the usages of speech, and this also to the extent from which even 
Grammar has maintained its freedom. Grammar, the science pro- 
per, — the nomology, of language, has not established ellipsis as a 



APPENDIX. 291 

thii'd law beside Concord and Government ; nor lias it even allowed 
Concord or Government to be superseded by ellipsis. And why ? 
Because the law, though not externally expressed in language, was 
still internally operative in thought. Logic, on the contrary, the 
science proper, — the nomology, of thought, has established an im- 
perative ellipsis of its abstract forms in conformity to the precari- 
ous ellipses of outward speech ; and this, although it professes to 
look exclusively to the internal process, and to explicate, — to fill 
up what is implied, but not stated, in the short cuts of ordinary 
language. Logic has neglected, — withheld, — in fact openly sup- 
pressed, one-half of its forms, (the quantification of the predicate 
universally in afiirmatives, particularly in negatives), because 
these forms, though always operative in thought, were usually 
passed over as superfluous in the matter of expression. 

Thus has logic, the science of the form, been made hitherto the 
slave of the matter, of thought, both in what it has received and in 
what it has rejected. And well has it been punished in its servi- 
tude. More than half its value has at once been lost, confusion 
on the one hand, imperfection on the other, its lot ; disgust, con- 
tempt, comparative neglect, the consequence. To reform Logic, 
we must, therefore, restore it to freedom ; — emancipate the form 
from the matter ; — we must, I'', Admit nothing material under 
the name of formal, and, 2°, Reject nothing formal under the 
name of material. When this is done, Logic, stripped of its acci- 
dental deformity, walks forth in native beauty, simple and com- 
plete ; easy at once and useful. 

It now remains to show that the quantities of the Predicate de- 
nounced by logicians are true logical forms. 

-s * * -X- * * 

The logicians have taken a distinction, on which they have de- 
fended the Aristotelic prohibition of an overt quantification of the 
predicate ; the distinction, to wit, of the formal, in opposition to 
the material, — of what proceeds vi formce, in contrast to what 
proceeds vi materia. It will be requisite to determine explicitly 
the meaning and application of these expressions ; for every 
logical process is formal, and if the logicians be correct in what 
they include under their category of material, the whole system 
which I would propose in supplement and correction of theirs, 
must be at once surrendered as imtenable. 



292 APPENDIX. 

In the first place, the distinction is not estahlished, in terms at 
least, by Aristotle. On the contrary, although the propositional 
and syllogistic relations which he recognises in his logical precept 
be all formal, he, as indeed all others, not unfrequently employs 
some which are only valid, say the logicians, vi materice, and not 
ratione formce^ that is, in spite of Logic. 

But here it is admitted, that a distinction there truly us ; it is, 
consequently, only necessary, in the second place, to ascertain its 
import. What then is meant by these several principles ? 

The answer is easy, peremptory, and unambiguous. All that is 
formal, is true as consciously necessitated by the laws of thought ; 
all that is material, is true, not as necessitated by the laws of 
thought, but as legitimated by the conditions and probabilities dis- 
coverable in the objects about which we chance to think. The one 
is a priori, the other a posteriori ; the one is necessary, the other 
contingent ; the one is known or thought, the other unknown or 
unthought. 

Por example ; if I think that the notion triangle contains the 
notion trilateral, and again that the notion trilateral contains the 
notion triangle; in other words, if I think that each of these is 
inclusively and exclusively applicable to the other ; I formally say, 
and, if I speak as I think, must say — All triangle is all trilateral. 
On the other hand, — if I only think that all triangles are trilateral, 
but do not think all trilaterals to be triangular, and yet say, — All 
triangle is all trilateral, the proposition, though materially true, 
is formally false. 

Again, if I think, that this, that, and the other iron-attracting 
stones are some magnets, and yet thereon overtly infer, — All 
magnets attract iron ; the inference is formally false, even though 
materially not untrue. Whereas, if I think that this, that, and the 
other iron-attractijig stones are all magnets, and thence conclude, — 
All magnets attract iron ; my conclusion is formally true, even 
should it materially prove false. 

To give the former example in an abstract notation : If I note 
C : B1 IIII : r, I may formally convert the proposition and state 
Y : teaa» — : C. But if I note C : b»- — r, I cannot formally 
convert it ; for the F niay mean either : r or > F ; and if I do, 
the product may or may not be true according as it is accidentally 



APPENDIX. 293 



applied to this or that particular matter. As to the latter ex- 
ample : C, ■■ » : (m m' m," &c.) :- : r 



This syllogism is formally legitimate. But, to take the following 

antecedent : this, if formally drawn, warrants only, (1), a particular 

conclusion ; and if, (2), a universal be drawn, such is logically null : 

C, »■ : (m m' m" &c.) : wb, r 

This being the distinction of formal and material, — that what 
is formally true, is true by a subjective or logical law ; — that what 
is materially true, is true on an objective or extra-logical condition ; 
the logicians, with Aristotle at their head, are exposed to a double 
accusation of the gravest character. For they are charged : — 1°, 
Tliat they have excluded, as material, much that is purely formal ; 
2°, That they have included, as formal, much that is purely material. 
Of these in their order. 

1°, I shall treat of this under the heads of Affirmative and of 
Negative propositions. 

Of the four Affirmative relations of concepts, as subject and 
predicate ; to wit — 1, The Toto-total ; 2, The Toto-partial ; 3, The 
Parti-Total ; 4, The Parti-Partial ; one half (1, 3) are arbitrarily 
excluded from logic. These are, however, relations equally neces- 
sary, and equally obtrusive in thought, with the others ; and, as 
formal realities, equally demand a logical statement and considera- 
tion. Nay, in this partial proceeding, logicians are not even self- 
consistent. They allow, for example, the toto-jyartial dependency 
of notions, and they allow of their conversion. Yet though the 
terms, when converted, retain, and must retain, their original re- 
lation, that is, their reciprocal quantities ; we find the logicians, 
after Aristotle, declaring that the predicate in affirmative proposi- 
tions is to be regarded as particular ; howbeit, in this instance, 
where the toto-partial is converted into the parti-total relation, 
theu' rule is manifestly false. When I enounce, — All man is 
animal, I mean, — and the logicians do not gainsay me, — All man 
is some animal. I then convert this, and am allowed to say, — 

o For an exjilanation of the notation gism, see below, Appendix XI, — Ed, 
here employed, in reference to Syllo- 



294 APPENDIX. 

So)ne animal is man. But I am not allowed to say, in words, 
though 1 say, — indeed must say, in thought, — Some animal is 
all man. And why ? Simply because there is an old traditionary 
rule in Logic, which j^rohibits us in all cases, at least of affirmative 
pro230sitions, to quantify the predicate universally ; and to estab- 
lish a reason for this exclusion, the principle of materiality has 
been called in. But if all is formal which is necessitated by thought, 
and if all that is formal ought to find an expression in Logic, in 
that case, the universal quantification of the notion, when it stands 
as predicate, may be, ought, indeed, on demand, to be, enounced, 
no less exjilicitly than when it stood as subject. This quantifica- 
tion is no more material on the one alternative than on the other ; 
it is formal in both. 

In like manner, the toto-total relation is denounced. But a 
similar exposition shows that notions, thought as reciprocating or 
coequal, are entitled, as predicate, to have a universal quantifica- 
tion, no less than as subject, and this formally, not materially." 

Li regard to the four Negative relations of terms, — 1. The Toto- 
total,— 2. The Toto-partial,—'^. The Parti-total,— k The Parti- 
partial; in like manner, one half, but these wholly different 
classes, (3, 4), are capriciously abolished. I say capriciously ; for 
the relations not recognised in Logic are equally real in thought, 
as those which are exclusively admitted. Why, for example, may 
I say, as I think, — Some animal is not any man ; and yet not 
say, convertibly, as I still think, — Any man is not some animal? 
Por this no reason, beyond the caprice of logicians, and the elisions 
of common language, can be assigned. Neither can it be shown, 
as I may legitimately think, — Some animal is not some animal, 
(to take an extreme instance), that I may not formally exjiress the 
same in the technical language of reasoning. 

In these cases, to say nothing of others, the logicians have, 
therefore, been guilty of extruding from their science much that 
is purely formal ; and this on the untenable plea, that what is 
formal is material. 

a. It is hardly requisite to notice the ojnnion is explicitly renounced by the 

blundering doctrine of some authors, acuter logicians, when they have chanced 

that the predicate is materially quantified, to notice the absurdity. — See Fonseca, 

even when predesignated as universal. Instit. Dial. 1. vi., c. 20. 
It is sufBcient to observe that this 



APPENDIX. 295 

(2). Special. 

Two objections have been taken to the universal quantification 
of the predicate. It is said to be— 1°, False; 2°, If not false, 
useless. 

I. The first objection may be subdivided into two heads, inasmuch 
as it may be attempted to establish it, a), on material ; b), on 
formal, grounds. Of these in their order : — 

a). This ground seems to be the only one taken by Aristotle, 
who, on three (perhaps on four) different occasions denounces the 
universal quantification of the predicate (and he but implicitly 
limits it to affirmative propositions), as " aliuays untrue^"- The 
only 23roof of this imexclusive denunciation is, however, one special 
example which he gives of the falsity emerging in the proposition, 
— All man is all animal. This must be at once confessed false ; 
but it is only so materially and contingently, — argues, therefore, 
nothing for the formal and necessary illegitimacy of such a quanti- 
fication. As extra-logical, this proof is logically incompetent ; for 
it is only because we happen, through an external knowledge, to 
be aware of the relations of the concepts, man and animal, that 
the example is of any import. But, because the universal quanti- 
fication of the predicate is, in this instance, materially false, is such 
quantification, therefore, always formally illegal ? That this is not 
the case, let us take other material examj)les. Is it, then, materially 
false and formally incompetent, to think and say, — All human is 
all rational, — All rational is all risible, — All risible is all capa- 
ble of admiration, — All trilateral is all triangular, — All trian- 
gular is all figure with its angles equal to turn right angles, &c. ? 
Or, employing Aristotle's material example, is it untrue, as he 
asserts, to say — Some animal is all man ; and this either collec- 
tively, — A part of the class animal is the whole of the class man, 
— or distributivehj, — Some several animal is every several man. 

But the absurdity of such a reasoning is further shown by the 
fact, that if it were cogent at all, it would equally conclude against 
the validity of the universal quantification of the subject. For 
this proposition is equally untrue (employing always Aristotle's 
own material example), — All animal is man. 

After this, it may the less surprise us to find that Aristotle 

« See below, p, 298.— Ed. 



296 APPENDIX. 

silently abandons liis logical canon, and adheres to truth and nature. 
In fact, he frequently does in practice virtually quantify the predi- 
cate, his common reasonings often proceeding on the reciprocation 
or coextension of subject and predicate. Nay, in his logical 
system, he expressly recognises this coextension ; unless, indeed, 
we overtly supply the quantification of the predicate, his doctrines 
of Induction and of Demonstration proper have no logical nota- 
tion ; and, unless we covertly suppose it, they are actually arrested. 
His definitions of the Universal, as severally given in his Prior 
and Posterior Analytics, are, in this respect, conflictive. In the 
former, his universal, (known in the schools as the Universale 
Prioristicum), explicitly forbids, whereas the latter, (the Univer- 
sale Posterioristicum of the schoolmen), implicitly postulates, the 
quantification of the predicate. 

b). The defect in the polemic of their master was felt by his 
followers. They, accordingly, in addition to, but with no correc- 
tion of, Aristotle's doctrine, argue the question on broader ground ; 
and think that they disjirove the formal validity of such quantifi- 
cation by the following reasoning. Overlooking the case, where 
the subject is particularly, the predicate universally, quantified, as 
in the instance I have just given, they allege the case of what are 
called reciprocatiiig propositions, where both subject and predicate 
are taken in their utmost extension, vi materiw, as subsequent 
logicians " say, but not Aristotle. In this case, then, as in the 
example. All man is all risible, they assert that the overt quanti- 
fication of the predicate is inept, because, the all as applied to 
the subject being distributively taken, every individual man, as 
Socrates, Plato, &c., would be all, (that is, the whole class), risible. 
This objection is only respectable by authority, through the great, 
the all but unexclusive, number of its allegers ; in itself it is futile. 

Terms and their quantifications are used either in a distributive, 
or in a collective, sense. It will not be asserted that any quantifi- 
cation is, per se, necessarily collective or necessarily distributive ; 
and it remains to ascertain, by rule and relation, in which signi- 
fication it is, or may be, employed. Now a general rule or postu- 
late of logic is, — That in the same logical unity, (jDroposition or 
syllogism), the same term or quantification should not be changed 

a, [See, for example, Pacius, In An. In An. Prior, L. i., c. 9, and above, p. 
Prior, L. i., c. 5, p. 134. Alexander, 274, note a, sm5. /».] 



APPENDIX. 297 

in import.a If, therefore, we insist, as insist we ouglit, that the 
quantification here, all, should be used in the same proposition 
ill the same meaning, that is, as applied to the one term, collec- 
tively or distributively, it should be so applied likewise to the 
other, the objection fails. Thus taken collectively: — All, (that 
is, the whole class), man is all, (that is, the whole class), risible, 
the projiosition is valid. Again, taken distributively : — All, (that 
is, every several), man is all, (that is, every several), risible, the 
proposition is, in like manner, legitimate. It is only by violating 
the postulate, — That in the same logical unity ^ the same sign or 
luord should be used in the same sense, that the objection applies ; 
whereas, if the postulate be obeyed, the objection is seen to be 
absurd. 

It is hardly necessary to say anything in confutation of the 
general doctrine, that in Reciprocating propositions the predicate is 
taken in its full extent, vi materice. In the first place, this doc- 
trine was not promulgated by Aristotle ; who frequently allowing, — 
frequently using, — such propositions, implicitly abandons the rule 
which he explicitly lays down in regard to the non-predesignation 
of the predicate by a imiversal. In the second place, apart from 
authority, such doctrine is in itself unfounded. Por as form is 
merely the necessity of thought, it is as easy to think two notions 
as toto-totally coinciding, (say, triangle and trilateral), as two 
notions toto-j)artially and parti-totally coincidmg, (say, triangle 
and figure). Accordingly, we can equally abstractly represent their 
relations both by geometric quantities, (lines or figures), and by 
purely logical symbols. Taking lines : — the former i ; the 

latter I . Taking the symbols, the former C : i— : F ; 

the latter A, esb=— — : B. But if the reciprocation were deter- 
mined by the mere matter, by the object contingently thought 
about, all abstract representation would be impossible. So much 
for the first objection, — that the universal quantification of the 
predicate would, at least in afiirmative propositions, be false. 

II. As to the second objection, that such quantification would 
be useless and superfluous, disorderly, nay confusive, this only 
manifests the limited and one-sided view of the objectors, even 
though Aristotle be at their head. 

* See above, p. 253. — Ed. 



298 APPENDIX. 

Is it useless in any case, theoretical or practical, that error be 
refuted, truth established ? And in this case : — 

1°, Is it disorderly and confusive, that the doctrine of Expon- 
ihles, as they are called, should be brought back from anomaly 
and pain to ease and order, — that propositions Exclusive and 
Exceptive, now passed over for their difficulty, and heretofore 
confessedly studied as " opprobria and excruciations," should be 
shown to be, not merely reducible by a twofold and threefold tor- 
tuosity, through eight genera and eight rules, but simple, though 
misunderstood, manifestations of the universal quantification of 
the predicate ? "" 

2", Is it useless to demonstrate that every kind of proposition 
may be converted, and not some only, as maintained by Aristotle 
and the logicians? And is it disorderly and confusive, in all 
cases, to abolish the triple (or quadruple) confusion in the triple 
(or quadruple) j)rocesses of Conversion, and to show, that of these 
processes there is only one legitimate, and that, the one simple of 
the whole ? 

3°, Is it disorderly and confusive to abolish the complex confu- 
sion of Mood and Figure, with all their array of rules and excep- 
tions, general and special ; and thus to recall the science of reason- 
ing to its real unity ? 

4°, Is it useless and superfluous to restore to the science the 
many forms of reasoning which had erroneously, inefi'ectually, and 
even inconsistently, been proscribed ? 

5°, Is it useless or sujierfluous to prove, that all judgment, and, 
consequently, all reasoning, is simply an equation of its terms, and 
that the diflerence of subject and predicate is merely arbitrary ? 

6°, In fine, and in sum, is it useless or siq^erfluous to vindicate 
Logic against the one-sided views and errors of logicians, to recon- 
cile the science with truth and nature, and to reestablish it, at 
once, in its amplitude and simplicity ? 

{g) — HisTOEicAL Notices of Doctkine of 
Quantified Peedicate. 

I. — Afjstotle. 
It will be sufficient to make one extract from Aristotle in illus- 

o See above, p. 2C1. — Ed. 



APPENDIX. 299 

tration of his doctrine upon this point, and I select the following 
passage from his Categories, c. v. § 7- 

" Further, the primary substances, [Trpwrat ovcriai, — individual 
existences], — because they are subjects to all the others, and as all 
the others are predicated of, or exist in, them, — are, for this reason, 
called substances by pre-eminence. And as the primary sub- 
stances stand to all the others, so stands the Species to the Genus. 
For genera are predicated of species, hut not, conversely, species 
of genera; so that of these two, the species is more a substance 
than the genus." 

Ammonius, who has nothing in his Commentary on the Cate- 
gories relative to the above passage of Aristotle, states, however, 
the common doctrine, with its reasons, in the following extract 
from his Conmientary on Porphyry's Introduction, (£ 29, ed. Aid. 
1546). 

" But confining ourselves to a logical consideration, it behoves 
us to inquire, — of these, which are subjected to, which predicated 
of, the others ; and to be aware, that Genera are predicated of 
Differences and Species, but not conversely. These, as we have 
said, stand in a certain mutual order, — the genus, the difference, 
and the species ; the genus first, the species last, the difference in 
the middle. And the superior must be predicated of the inferior ; 
for to jDredicate the inferior of the superior is not allowable. If, 
for examj)le, we say, — All man is animal, the proposition is true ; 
but if we convert it, and say, — All animal is man, the enounce- 
nient is false." Again, if we say, — All horse is irrational, we are 
right ; but if conversely we say, — All irrational is horse, we are 
wrong. For it is not allowed us to make a subject of ^the acci- 
dental. Hence is it incompetent to say that Animal is man, as 
previously stated." 

[Categ. ch. ii. § 1. 

" When one thing is predicated of another as of its subject, all 
that is said [truly] of the predicate will be said [truly] also of 

a The converse of a true proposition animal, and, All horse is some irra- 
is always truej but the false proposi- tional. Convert these, — Some animal 
tions which are here given, as conver- is all man, and, So)ne irrational is all 
sions of the true, are not conversions horse; the truth remains, but the one- 
at all. The true propositions, if ex- sided doctrine of the logicians is ex- 
plicitly stated, are, — All man is some ploded. 



800 APPENDIX. 

the subject. Thus man is predicated of this and that man,'^ and 
animal of man ; animal will therefore be predicated of this and 
that individual, for this and that individual is both man and 
animal." 

De Interpret, c. vii. § 2-4. ; see also c. x. 

" To enounce something of a universal universally, I mean as, 

All or every man is white, No man is white 

To enounce something of universals not universally, I mean as, 
Man is white, Man is not ivhite ; for whilst the term man 
is universal, it is not used in these enouncements as universal. 
For all or every (770,9) does not indicate the universal [itself], 
but that [it is applied to a subject] universally. Thus, in 
reference to an universal predicate, to predicate the universal, is 
not true. Por no affirmation is true, in which the universal is 
predicated [of an universal predicate], as, All or every man is all 
or every animal." (See Ammonius, Boethius, Psellus, Magentinus, 
&c). 

Prior Analytics, Bk. I. c. 27, §. 9. "The consequent [i.e. the 
predicate] is not to be taken as if it wholly followed [from the 
antecedent, or subject, exclusively]. I mean, for example, as if 
all [or every'] animal [were consequent] on man, or all [or every^ 
science on m,usic. The consequence simply [is to be assumed], as 
in our propositions has been done ; to do otherwise (as to say that 
all [or every] man is all [or every] animal, or that justice is 
all [or every] good, is useless and impossible ; but to the antece- 
dent [or subject] the all or [every] is prefixed." 

Posterior analytics, B. I. c. xii. § 10. "The predicate is not 
called all [or every ] ; [that is, the mark of universality is not 
annexed except to the subject of a proposition]. 

In refutation of Aristotle's reasoning against the universal j^re- 
designation of the predicate — it will equally disprove the universal 
predesignation of the subject. For it is absurd and impossible to 
say, All animal is man; All (every) immortal is the soul; 
All 2}leasure is health; All science is music; All motion is 
pleasure.^ But in point of fact such examples disprove nothing ; 
f(jr all universal predesignations are applicable neither to subject 

a. [For the rh here, as el.sewhere, de- )3 Examples from Wegelin, In Grcj. 
notes the indlviduum signatum, not the Aneponymi Comp. Phil. Sijnt. L. iv. c. 
indlviduum vagum.] 1, p. 473; L. vi. c. 1, p. G73. 



APPENDIX. 



301 



nor predicate, nor to both subject and predicate — are thoughts not 
things; and so are all 2^redesignations ; therefore, &c. It is only 
marvellous that such examples and such reasoning could satisfy the 
acutest of intellects ; that his authority should have imposed on 
subsequent logicians is less wonderful a] 

Quantification of Predicate — Aristotle. 

1. Admits that syllogism mental not oral (An. Post. I. 10). This 
to be borne in mind. 

2. That individual is never predicated, (Cat. c. 2), refuted by re- 
ciprocation of singular, (An. Pr\ ii. 23, § 4). 

3. That affirmative universal not [to] be added to predicate, incom- 
patible with what he says of reciprocation, (in An. Pr. ii. cc. 
22 and 23 alibi). That his custom to draw universal conclu- 



a And here I may correct an error, as 
I conceive it to be, which has descended 
fi'om the oldest to the most recent in- 
terpreters of the Organon, and been 
adopted implicitly by logicians in gene- 
ral. It is found in Alexander and 
Ammonius, as in Trendelenburg, Saint- 
Hilaire, and Waitz ; nor indeed, as far 
as I know, has it ever been called in 
question during the interval. It regards 
the meaning of the definition elevated 
into a two-fold axiom, the esse in toto, 
&c., and did de omni, &c., toward the 
conclusion of the first chapter of the 
first book of the Prio7' Analytics. 1h Se 
(V o\(f! elvai fT€pov erepaj Kol rh Kara 
■wayTos KaTrjyopeladaL OaT^povdarepourav- 
t6v icrriv. This, with its ambiguity, may 
be thus literally, however awkwardly, 
translated : — " But [to say] that one 
thing is in a whole other, and [to say] 
that one thing is predicated of all an- 
other, are identical." — Now, the question 
arises, — What does Aristotle here mean 
by " a whole other V for it may signify, 
either the class or higher notion under 
which an inferior concept comes, or the 
inferior concept itself, of which, as of a 
subject, the higher is predicated. The 
former is the sense given by all the 
commentators; the latter, the sense 



which, I am confident, was intended by 
Aristotle. 

There are only two grounds of inter- 
pretation. The rule must be expounded 
in consistency — 1°, "With itself ; 2°, Must 
be with the analogy of Aristotelic usage. 

1°. On the former ground, the com- 
mon doctrine seems untenable; for what 
Aristotle declares to be identical, by that 
doctrine becomes difi'erent, nay ojiposed. 
An inferior concept may be in a higher 
whole or class, either partially or totallj' ; 
and the definition on the prevalent in- 
terpretation virtually runs — " To say 
that one thing is all or ^Mrt in the whole 
of another, and to say that this other 
is predicated of it unexclusively, are 
convertible." Had Aristotle, therefore, 
used the expression in the signification 
attributed to him, he must, to avoid the 
contradiction, have said — T^ Se izav 
erepoy iv oXc^ elvai ^repcp k.t.A. (" But 
to say that one thing is all in a whole 
other," &c.) 

2°. On the second ground, it may, 
however, be answered, that the ambi- 
guity of the word, as it stands, is super- 
seded, its signification being determined 
by other passages. I join issue ; and on 
this ground am well content to let the 
question be decided. 



302 



APPENDIX. 



sions in Thiixl Figure and affirmative in Second'' with allow- 
ance of simple conversion in certain universal affirmatives. 
That particular not in negative predicate, absurd in ov Tras, 
non omnis. 



Aristotle's doctrine of Predesignation. 

1°, How can Aristotle, on his doctrine, make universal terms taken 
indifferently, or without predesignation, be tantamount to parti- 
culars? {An. Prior, I. c. 4, § 13, Org. Pacii, p. 135, alibi), 

2°, An. Prior, 1, c. 27, § 7. He says, as elsewhere, " a proposi- 
tion being indefinite, [preiu designate], it is not clear whether it be 
universal ; when, however, it is definite, [predesignate], that is 
manifest." Contrast this statement with his doctrine of the all. 

3°, There are syllogisms in Aristotle, which are only valid 
through the quantity of the predicate./^ 

4°, Aristotle requires, though he does not admit, the universal 



In the first place, the meaning I attri- 
bute to the expression, " wlwle other " — - 
that is, whole subject or inferior notion, 
is, in short, in strict conformity with 
Aristotle's ordinary language. There 
are, I admit, sundry passages in his logi- 
cal writings, where the term whole is 
clearly used as synonymous with class 
or higher notion ; as, to limit ourselves 
to the Prior Analytics, in Book I. iv., § 
2 ; and II. i. § 4. But, every single text, 
in which the term whole appears in this 
relation, is overruled by viore than five 
others, in which it is no less clearly ap- 
plied to denote the totality of a lower 
notion, of which a higher is predicated — 
passages in which the word whole (ciAos) 
is used convertibly with all (ttSs). See 
for example, A n. Pr. II. ii., § 5, § 1 6 — iii. 
§ 5, § 7 {his.), § 13 [his.], § 14, § 15-iv. § 
6 {bis.), § 8, § 10, § 12 (iM.)— xxii. § 7, § 
8 — xxiii. § 4. 

But in the second place, (and this is 
directly subversive of the counter-opi- 
nion, even in the principal of the few 
passages where the term ivhole is used 
for class), the lower notion may be in 
or under the higher, only 2Mrticularly ; 
and this manifestly shows that Aristotle 
c<juld not possibly mean, by merely 



saying, that one thing is another, as in a 
class, that it is so unexclusively, or uni- 
versally. Compare An. Pr. I. iv. §§ 2, 
3, 1 0. On this interpretation, Darii and 
Ferio would then be annulled ; a special 
result which ought to have startled the 
logicians into a doubt of the accuracy 
of the received doctrine in general. (See, 
instar omnium, Pacius, in his relative 
Notes and Commentary.) 

That doctrine must, therefore, be aban- 
doned, and the rule reduced to a defini- 
tion, read in the following signification : 
— " But to say that one thing is in the 
whole of another, as in a subject, and to 
predicate one thing universally of another, 
are merely various expressions of the 
same meaning." This, in fact, is just 
the preliminary explanation of the two 
oi'dinary modes of stating a proposition, 
subsequently used by Aristotle. Here,in 
both convertibles, he descends from ex- 
tension to comprehension, from the pre- 
dicate to the subject; and the ingenious 
exposition by the commentators, old and 
new, of the inverse intention of the phi- 
losopher in the two clauses, must be re- 
garded as erroneous. 

a See below, p. 346. — Ed. 
/8 See below, p. 346.— Ed. 



APPENDIX. 803 

predesignatioii of the predicate in his syllogism of Induction. Vide 
An. Prior., L, ii., c. 23, § 4, Organon Pacii, p. 399. Compare 
also his doctrine, p. 396.) 



II. Alexandek Aphrodtsiensis. 

Alexander Aphrodisiensis, in his commentary on the first book 
of the Prior Analytics, and in reference to the second passage of 
Aristotle, states as follows : 

"And in the book of Enouncement Aiistotle explains, why he 
there says : — ' that to predicate the universal of a universal predi- 
cate is not true ; for there will be no proposition, if in it we pre- 
dicate the universal of the universal, as, All man is all animal.' 
He repeats the same also here ; showing, how it is useless to 
attempt thus to express the consecution, [of higher from lower 
notions] ; and adds, that it is not only useless, but impossible. 
For it is impossible, that all man should be all animal, as 
\_useless to say, {a)(pr)(TTOv eiireiv must have dropt out)], that all 
man is all risible. We must not, therefore, apply the all to the 
consequent, [or predicate], but to that from which it follows, [or 
subject]. For man is to be taken universally, as that from which 
animal follows, supposing this to be the consequent of all man. 
Thus shall we obtain a stock of universal jiropositions. The process 
is the same, in making man the consequent on its proper all; 
but man is not consequent on all biped, but on all rational. 

" The words, ' as we express ourselves,' mean — as we express 
ourselves in common usage. For we say, that all man is simply, 
animal, and not all animal, and that all pleasure is natural, not 
all natural; prefixing the all, not to the consequent, but to the 
subject from which the predicate follows." {Edd. Aid., f. 100 a; 
Junt., f. 122 a ; Compare Aid., f. 86 a ; Junt, f. 105 a.) 

III. — Ammonius Heemi.e. 

Ammonius Hermife, In de Tnterp. c. vii. § 2. (Aldine edi- 
tions, of 1503, sig. C. vii. 59, of 1546, ff. 70, 74). 

" In these words Aiistotle inquires : — Whether, as the an- 
nexation of the affirmative predesignation (TTjOocrStoptcr/xo?) to the 



304 APPENDIX. 

subject constitutes one distinct class of propositions, the same 
annexation to the predicate, may not, likewise, constitute another ; 
and he answers, that the supposition is absolutely groundless. 
Thus the enouncement — all (or every) man is all (or every) ani- 
7nal, (tto,? dvOpcoTTOs ttou Ifiiov ecm) ; asserts that each man is 
all animal — as horse, ox, &c. But this proposition is impos- 
sible ; as is shown by Aristotle in his here omitting the word 
' true.' For no affirmation can be true, in which the universal is 
predicated of a universal predicate ; that is, in which the universal 
predesignate is added to a universal predicate ; as when we say 
that man (of whom all, or, as he says, universally, animal is 
predicated), is not simply animal, but all animal. He, therefore, 
teaches, that such an affirmation, as utterly untrue, is utterly in- 
competent 

" Neither does Aristotle allow the predesignation some to be 
annexed to the predicate, that propositions may, thereby, become 
true always or occasionally. For logicians, (as they do not pro- 
]DOse to themselves every superfluous variety of enunciation), are 
prohibited from considering propositions, (not only those always 
true or always false), but those which express no difference in re- 
ference to necessary or impossible matter, and afford us absolutely 
no discrimination of truth from falsehood. Thus, particular pro- 
positions, which may be alternatively true and false, ought not to 
have a predesignated predicate. For in a proposition, which has 
all their power, without any predesignation of its predicate ; why 
should we prefer to the simpler expression, that which drags about 
with it a superfluous additament ? Why, for example, instead of — 
All man is some animal, [I read, tl ^(oov], or. All man is not all 
animal,"" should we not say — All man is animal, and in place of 
All man is no stone, not say, — All man is not stone ; or, what 
is a simpler and more natural enouncement still, — Ko man is stone. 

"And when we find some of the aiicients teaching that the 
particular affirmative predesignation is to be connected with the 
predicate, as when Aristotle himself styles the soul a certain {some) 

a It will be observed, that Ammo- trine; and this impossibility itself ought 

nius does not attempt an equivalent for to have opened his eyes upon the insuf- 

this proposition. In fact it is impos- ficiency of the view he maintained, 
sible on the common or Aristotelic doc- 



APPENDIX. 305 

entelecliT, JfTekexeLoiv Tiva\ and Plato, rhetoric, a certain (soine) 
experience. [ifJureLpiav tlvo) ; it is to be observed that the some 
is there added for the sake of showing, that the predicate is not 
convertible with the subject, but is its genus, and requires the 
adding on of certain differences in order to render it the subject's 
definition. 

" But, add they, is not the reasoning of Aristotle refuted by 
fact itself, seeing that we say, All man is capable of all science : 
thus truly connecting the universal predesignation with the uni- 
versal predicate ? The answer is this : — that, in truth it is not the 
predicate to which we here annex the all For what is predi- 
cated, is what is said of the subject. But what is here said of 
man is. not that he is science, but that he is capable of science. 
If, therefore, the all were conjoined with the capable and the 
proposition then to remain true, as when we say — all man is all 
capable of science; in that case, the reasoning of Aristotle would 
be refuted. But this proposition is necessarily false. It, in fact, 
asserts nothing less, than that of men, each individual is all 
the kind ; — that Socrates is not Socrates only, but also Plato, 
Alcibiades, and, in short, every other man. For. if all man is all 
capable of science, Socrates beiug one of the all, is, therefore, 
himself all capable of science ; so that Socrates will be Plato, 
Alcibiades, &c., since they also are capable of science. For if 
Socrates be not, at once, Plato, Alcibiades, &c., neither wiU he be 
all capable of science 

■' Xow, that we ought not to prefix the universal affirmative pre- 
designation to the predicate, (whether the predicate be more gene- 
ral than the subject, as All man is all animal, or, whether they be 
co-adequate, as All man is all risible,) — this is manifest from 
what has been said. Even when the terms are coadequate or re- 
ciprocating, the proposition runs into the absurd. For, declaring 
that all man is all risible, it virtually declares, that each indi- 
vidual man is identical with all men ; that Socrates, in that he is 
a man, is all 7'isihle, consequently, all man 

" But why is it, that the predicate is intolerant of the predesig- 
nation all. though this be akin to the counter-predesignation no 
or none ? Is it because the affii'mative predicate, if predicated 
universally, tends always to contain under it tlie subject, and this 
not only when itself coadequate with the subject, but when trans- 

VOL. II, U 



30G APPENDIX. 

cending the subject in extension ; while, moreover, through a parti- 
cipation in its proper nature, it is suited to bind up and reduce to 
unity the multitude of individuals of which the subject is the 
complement ? For, as Aristotle previously obseiTcd — ' The all 
does not indicate the universal, but that [the universal predicate 
inheres in, or is attributed to, the subject] universally.' If, there- 
fore, the affirmative predicate thus tend to collect into one what 
are by nature distracted, in virtue of having been itself previously 
recognised as simple ; in this case, the all, [superadded to this 
universal predicate, in fact], enounces not a unity, but a multitude 
of several things, — things which it is manifestly unable to compHcate 
into recij)rocity. But, on the other hand, since what is negatively 
predicated of, is absolutely separated from, the subject ; we are, 
consequently, enabled to deny of the subject all under the predicate, 
as in saying. All vian is no stone. We may indeed condense 
this proposition, and say more simply. All man is not stone ; or 
more simply still. No man is stone ; thus dispensing with the 
affirmative j)redesignation in a negative proposition." 

IV. — BOETHIUS. 

Boethius,/w Lihrum de Interpretatione, editio secunda,et in tex- 
tum laudatum. Opera, jj. 848. 

" What he says is to this purport : — Every simple proposition 
consists of two terms. To these there is frequently added a de- 
termination either of universality or of particularity ; and to 
which of the two parts these determinations are to be added, he 
expounds. It appears to Aristotle that the determination ought 
not to be conjoined to the predicate term ; for in this proposition, 
Man is animal — {Homo est animal) it is inquired whether the 
determination ought to be coupled with the determination, so that 
it shall be — (Oninis homo animal est) — All (or every) man is ani- 
mal ; or with the predicate, so that it shall be, — {Homo omne ani- 
mal est) — Man is all (or every) animal ; or with both tlie one and 
tlie other, so that it shall be. All (or every) man is all (or every) 
animal, {Omnis homo omne animal est). But neither of these 
latter alternatives is competent. For the determination is never 
joined to the predicate, but exclusively to the subject ; seeing 
that all predication is either greater than the sulyect, or equal. 



APPENDIX. 307 

Thus ill this proposition — All (or every) man is animal, (omnis 
homo oMimal est), animal [the predicate] is greater than man 
[the subject] ; and, again, in the proposition — Man is risible, 
(homo risihilis est), risible [the predicate] is equated to man [the 
subject] ; but that the predicate should be less and narrower than 
the subject is impossible. Therefore, in those predicates whichi are 
greater than the subject, as, for example, where the predication is 
animal, the proposition is manifestly false, if the determination of 
universality be added to the predicate term. For if we say, Man 
is animal, (homo est animal), we contract animal, which is greater 
than man^ by this determination to [an identity of extension with] 
man, the subject, although the predicate, animal, may be applied 
not only to man, but to many other objects. Moreover, in those 
[subjects and predicates] which are equal, the same occurs; for if I 
say. All (or every) man is all (or every) risible, (omnis homo omne 
risibile est), — in the first place, in reference to the nature of man 
itself, it is superfluous to adject the determination ; and, again, 
if this be added to all several men, the proposition becomes false, 
for when I say. All (or every) man is all (or every) risible, by this 
I seem to signify that the several men are [each of them] all or 
every risible, which is absurd. The determination is, therefore, to 
be placed not to the predicate but to the subject. But the words 
of Aristotle are thus reduced to the following import : — In those 
predicates which are universal, to add to them aught universal, 
so that tJie universal predicate may be predicated universally, 
is not true. For this is what he says — " In the case of a univer- 
sal predicate," (that is, in a proposition which has an universal pre- 
dicate), " to predicate the universal, itself universally, is not true.'" 
For in an universal predicate, that is, which is universal and is 
itself predicated, in this case universally to predicate the predi- 
cate which is universal, that is, to adject to it a determination of 
universality, is not true : for it cannot be that any affirmation 
should be true in which a universal determination is predicated of 
a predicate universally distributed ; and he illustrates the concep- 
tion of the matter by the example, " All or every man is cdl (or 
every) animal, (omnis homo omne animal est), of the incompe- 
tency of which we have already spoken." 

Boethius, In Librum de I nterpr elation e, editio prima. Opera, 



808 APrENDIX. 

p. 236. (Text so wretchedly printed that the sense must be con- 
stituted by the reader. ) 

[Aristotle, c. vii. § 4], " ' In what is predicated as an universal, 
to predicate the universal universally is not true/ 

" In this sentence he instructs us what is the place to which the 
determination of universality should be rightly added. For he 
teaches that the universality, which we call the universal determi- 
nation, is to be connected with the subject term, never with the 
predicate. For were we to say — All (or every) man is animal, 
{omnis homo animal est), we should say rightly, annexing the 
all (or every) to the subject, that is, to the term Tnan. But if we 
thus speak — All or every man is all or every animal, {omnis 
homo omne animal est), we should s-peak falsely. He, therefore, 
does not say this [in the words] — ' in what is predicated as an 
universal,' as animal of man ; for animal is universal, being pre- 
dicated of all or every man. [But he says] — To predicate this 
universal itself, anim^al, to wit, universally, so that we enounce 
— All (or every) animal is man, {omne animal esse hominerro), is 
not true ; for he allows this to be rightly done neither iii these nor 
in any other affirmation.* He adds, therefore ; — ' For no affirma- 
tion will be true in which a universal predicate shall be univer- 
sally predicated, as All or every man is all or every animal, 
{omnis homo est omne animal).' 

"Why this happens, I will exi^lain in a few words. The 
predicate is always greater than the subject, or equal to it. 
Greater, as when I say Han is animal, {homo animal est) ; here 
animal is predicated, man is subjected, for animal is predicated of 
more objects than man. Again, it is equal when we thus speak — 
Man is risible, {homo risibilis est) ; here man is the subject, 
risible the predicate. But man and risible are equal ; for it is 
proper to man to be a risible animal. But that the predicate 



a The Coimbra Jesuits (Sebastianus by their brother Jesuit, P. Vallius of 

Contus, 1606), erroneously make Boe- Rome, in his mighty Logic [ad locum). 

thiua and Averroes oppose Aristotle, With Boethius he joins Levigersonides ; 

" thinking that the sign of universality — he means the Rabbi Levi Ben Gerson, 

may be annexed to the predicate of a of Catalonia, who died at Perpignan in 

universal proposition, when it is coexten- 1370, who wrote on Theology, Philoso- 

sive with the subject," (arf locum ii., p. phy, Mathematics, and Logic. SeeJocher 

158). This, a mistake, has been copied v. Levi, from Bartolocci and Wolf. 



APPENDIX. 309 

should be found less than the subject, is impossible. Is the predi- 
cate the greater ? Then, to adject the universal to the predicate, is 
false, as in the example he himself has given — All (or every) man 
is all (or every) animal, {omnis homo omne animal est). Is it 
equal ? Then, the adjection is superfluous, as if one should say. All 
every man is all or every risible, [omnis homo omne risibile 
est). Wherefore, to predicate a universal predicate universally is 
incompetent." 



V. — AVEEKOES. 

Averroes, Perihermenias, L. I., c. v. 

" Propositions are not divided from the conjunction of the pre- 
designation (clausurse) with the predicate ; because the predesig- 
nation, when added to the predicate, constitutes a false or a super- 
fluous proposition : — False, as All or every man is all (or every) 
animal, (omnis homo est omne animal) ; suijerfluous, as All (or 
every) man is some or a certain animal, (omnis homo est quod- 
dam animal)." Vide Conimbricenses, In Arist. Dial., ii. lo8. 



VI. — Albeetus Magnus. 

Albertus Magnus, Periherminias, L. I., Tractatns, v. c. 1, (Op. 
ed. Lugd. 1651, t. I, p. 2G1). 

[" Ly ' oTunis' non est universale, sed signum universalitatis. 
Quare ly ' omnis' et hujusmodi signa distributiva non sunt uni- 
versalia, secundum Avicennam" ]. Hoc enim signum distri- 
butivum, quod est omnis, non est universale, proprie loquendo : 
sed est signum per quod stat pro particularibus universaliter uni- 
versale, cui tale signum est adjunctum. Causa autem, quare non 
sit universale, est : — quia, quamvis secundimi grammaticum sit 
nomen appellativura, hoc est, multis secundum naturae sure apti- 
tudinem conveniens ; tamen est, secundum formam, infinitum, 
nuUam enim naturam unam dicit. Propter quod omnis naturae 
communis est distributivum. Universale autem est, quod est in 
multis et de multis, su?e naturse, suppositis. Ideo omnis, et 
mdlus, et hujusmodi signa universalia esse non possunt ; sed 
sunt signa designantia utrum universale sit acceptum universaliter 



i 



310 appp:ndix. 

vel particiilariter, secundum sua supposita. Et ha?c sunt verba 
Avicennrei. 

[ " Quare signum universale non sit ponendum a parte 
prredicati.] In subjecto universali signum distributivura ordi- 
nandum : quia per divisionem subjecti, pmedicatum partibus 
attribuitur subjecti, ut divisim participent id per pradica- 
tionem, et non in praedicato ponendum : quia quum praedicatum 
formaliter sit acceptum, non proprie dividitur, nisi alterius, hoc est, 
subjecti divisione : sed insequaliter redditur subjecto et partibus 
ejus. Unde id quod est universale, preedicari potest, ut Omnis 
homo est animal ; sed universale universaliter acceptum non po- 
test prtedicari ; nulla enim vera affirmatio esse potest, in qua de 
universaK aliquo prsedicato predicetur sive prsedicatio fiat ; quo- 
niam universaliter sic patet, quod falsum est, Onmis homo est 
omne animal, et si ponatur, quod Nullum animal sit nisi homo. 
Cum enim homo subjiciatur gratia partium suarum, et pregdi- 
cata formaliter accipiantur, oportet quod Quilihet homo esset 
omnc animal, quod falsum est." 

VII— Levi Ben Geeson. 

Levi Ben Gerson (or Levi Gersonides), a Jewish philosopher, 
Avho died in 1370 at Per2)ignan, wrote commentaries on Averroes' 
Commentary upon the logical books of Aristotle. The following is 
what he says on Averroes' doctrine touching the quantification of 
the predicate, as it is found (f. 3D) of the Venice edition, in folio, 
of lo.52,a of the works of Aristotle and Averroes: — "Although 
it be not necessary that when the quantitative note is attached to 
the predicate, this should be false or superfluous, seeing that it 
may be neither, as when we say. All man is all rational ; and the 
same holds good in all other reciprocating propositions ; — never- 
theless, as in certain matters it may so happen, Aristotle has de- 
clared that the quantitative note is not to be joined to the predi- 
cate in any language. But it may be here objected, that if this 
be the case, the quantitative note should not be annexed even ta 
the subject, since there too it may be eitlier false or superfluous. 
Superfluous, — as when we say. Some animal is rational. For the 
very same follows here, as if we simply say, Animal is rational ; 

a Not iu the 8vo edition of these works. Venice, 1560. 



APPENDIX. 311 

the some, therefore, is superfluous. False, — as when we say, All 
animal is rational. The reason, therefore, assigned by Aristotle 
why the quantitative note should not be annexed to the predicate, 
is futile, seeing that for the same reason it should not be connected 
with the subject. To this we may answer: That the cause why 
the quantitative note is not usually conjoined with the predicate, 
is, that there would thus be two quassita at once, — to wit, whether 
the predicate were affirmed of the subject, and, moreover, whether 
it were denied of everything beside. For when we say. All man 
is all rational, we judge that all man is rational, and judge, like- 
wise, that rational is denied of all hut man. But these are in 
reality two different qua3sita ; and therefore it has become usual 
to state them, not in one, but in two several propositions. And 
this is self-evident ; seeing that a qupesitum, in itself, asks only — 
Does, or does not, this inhere in that ? and not — Does this inhere 
in that, and, at the same time, inhere in nothing else ? " 

VIII. — The Masters op Louvain. 

Facultatis Artiuin in Academia Lovaniensi Commentaria in 
Ai^istotelis Lihros de Dialectica,{loS5),Tr. iii. c. l,p. 162, ed.l547. 

Speaking of the text in the De Inter pretatione, the Masters, inter 
alia, allege : " But if it be even elegantly said by a poet — ' Nemo 
est omnis homo,' — ' Non omnes omnibus artes' — [proverb, ' Unus 
homo nuUus homo '], why may we not contradict this aptly, 
howbeit falsely, — ' Aliquis est omnis homo' ? Why, (tliey say), do 
you determine the predicate by the note of universality, seeing 
that the quantity of the proposition is not to be sought from the 
predicate, but from the subject ? We answer, because we wish 
to express a certain meaning in words, which by no others can be 
done. But if the mark of universality could only be employed in 
changing the quantity of propositions, it would not be lawful to 
annex it to the part of the predicate. We have, therefore, thought 
these few cautions requisite to evince that what is condemned by 
these critics for its folly, is not incontinently sophistical or foolish 
babbling. But as to the universal rule which Aristotle enounces, 
— 'No affirmation will be true,' &c. — it is sufficient if it hold good 
in the majority of cases; whether the predicate exceed the subject, 
as. All man is all animal, — be its equal, as, All man is all 7'isible, 



312 



APPENDIX. 



or its inferior, as, [So7ne] animal is all man. In a few cases, 
however, the exception is valid ; as, — This sun is every sun, One 
phoenix is all plicenix, and some others. Nor are these futile 
subtleties, since reason herself approves.'"' 



IX. — TiTIUS AND RiDIGEK. 

The only notice of these speculations of Titius,a which I have 
met with in any subsequent philosopher, (and I speak from an 
insijection of several hundred logical systems, principally by Ger- 
mans), is his friend Eidiger's ; who in his elaborate work De Sensu 
Veri et Falsi, first published some eight years subsequently, (in 
1709, but I have only the second edition of 1722), attempts a 
formal refutation of the heresy of a quantified predicate. It was 



a [Titius, Jrs Cogitandi, c. vi., has the 
following relative to the quantification 
of the predicate]: — § 36, " Licet autem 
Proi^ositionum quantitas ex Subjecto 
a3stimetur, attamen Prsedicatum nou 
penitus negligendum videbatur, ceu vul- 
go in hoc tractatione fieri solet, nam et 
hujus quantitatem observasse utile est, 
et crediderim et disquisitionis hujus 
neglectu varios eiTores tam in doctrina 
Conversionis, quam Syllogistica esse ex- 
ortos, quos suis locis videbimus. § 37, 
Breviter itaque observandum,in proposi- 
tionibus affirmativis, licet universalibus, 
prasdicatum plerumque esse particulare, 
tribuique subjecto secundum totam qui- 
dem suam compreliens'wnem, non vero 
ex ten si one m. § 39, E coutrario in propo- 
aitionibus negativis, licet particularibus, 
plerumque prasdicatum est uiiircrsale, 
ac tam secundum comiirehensionem 
quam extensionem suam totam, a sub- 
jecto removetur. § 41, Interim non pu- 
tarem affirmationem vel ncgationem 
ipsam diversam illam prajdicati quan- 
titatem necessario postulare, sed credi- 
derim potius, id omne a diverse rerum 
et idearum habitu oriri, affirmation! 
vero et negation! prredicati quantita- 
tem esse velut indiiTerentem. § 42, 
Nam plerumque prajdicata subjectis sunt 
latiora ; quodsi igitur ilia cum his com- 
ponas, non poterit nou prasdicatum jiar- 
ticulare iude emergere, dum unice ad 



subjectum restringi nequit, sed ad alia 
quoque extendi aptum manet. § 43, 
Ast si praidicatum a subjecto I'emoveas, 
universale illud erit, cum quicquid in 
ejus vel comprehensione vel extensione 
est ab hoc sejungatur, nee imminuit 
uuiversalitatem, quod idem ab aliis sub- 
jectis quoque removeatur, nam si prse- 
dicatum aliis etiam conveniat, tum qui- 
dem uni subjecto non potest dici uni- 
versaliter tributum, verum si de multis 
negetur, potest nihilominus de certo 
aliquo subjecto uuiversaliter quoque ne- 
gari. § 44, Quodsi habitus attributi 
permittat, poterit aliquando propositio 
affirmativa pra3dicatum universale, et 
negativa particulare habere ; nihil enim 
obstat, quo minus aliquando totum al- 
ter! jungere, vel partem ab eodem re- 
movere queas. § 45, Ha2C itaque pro- 
posititio : — Omnis homo est risibilis, 
habot pra?dicatum univei'sale, si risibili- 
tatem 2)ro homiuis proprio habeas; sicut 
ha3, — Nullus Turca est homo, (Scil. Chris- 
tkmus),ye\ Quidam mcdicus non esthomo 
quidam, pnedicatum particulare conti- 
nent, dum pars solum comprehensiouis 
et extensionis removetur." For the 
application, by Titius, of the principle of 
a quantified predicate to the doctrine of 
Conversion, see above pp. 274, 275; and 
to the theory of Syllogism, see below, 
p. 375, and Appendix, X. — Ed.] 



APPENDIX. 813 

only, however, after " the most manifest demonstrations of the 
falsehood of this novel prejudice had been once and again privately 
communicated to his very learned friend, " (Titius ?), that Kidiger 
became at length tired, as he expresses it, " of washing a brick," 
and laid the polemic before the f)ublic. It was not certainly the 
cogency of this refutation which ought to have thrown the counter 
opinion into oblivion ; but this refutation, such as it is, though 
with nothing new, is deserving of attention, as presenting the most 
elaborate discussion of the question to be met with, after Am- 
monius, and in modern times. But the whole argument supposes 
certain foundations ; and it will be sufficient to show that these 
are false, to dispose of the whole edifice erected upon them. I 
ought to mention, that it was Kidiger's criticism which first directed 
my attention to the original of Titius. 

" Origo autera hujus erroris neglectus notissimse acquivoca- 
tionis signorum omnis et quidam esse videtur, qua h?ec signa, 
vel collective sumi possunt, vel distributive. Priori modo, quan- 
titas in prsedicato concepta sensum quidem infert non penitus 
absurdum, cpeterum propositionem constituit identicmm et frus- 
traneam." Ridiger then goes on to a more detailed statement 
of what he supposes to be the grounds on which the erroneous 
opinion proceeds." 

First Case. — " Verbi gratia, Quoddam animal est omnis homo ; 
hoc est. Species qucedam animalis, homo nemioe, omne id, quod 
homo est : quod alium sensum, habere nullum potest, quam, quod 
omnis homo sit homo : sic autem collective sumitur et signum 
subjecti et signum prsedicati." This objection is absurd, for it is 
suicidal ; applying equally to the proposition which the objector 
holds for good, and to that which he assails as bad. All man is 
(some) animal. Here, is not animal or some animal, just a 
certain species of animal, and is not this species, man, to wit, all 
that is man, and nothing else ? There is, consequently, the same 
tautology in the one case as in the other ; and if we are blamed 
for only virtually saying, by the former. All man is man, does 
the objector say a whit more than this, by the latter ? Ridiger 
goes on : " Quodsi vel alteram signum, vel utrumque, distributive 
sumatur, semper absurdus erit propositionis sensus." 

« Second Edition, pp. 232, 302. 



314 APPENDIX. 

Second Case. — " Verbi gratia, sumatiir uti'umque signum distri- 
butive, sensus erit, Quoddam individuum animalis, (v. g. Fetrus,) 
est omne individuum hominis, (v, g. Davus, Oedipus)." This is a 
still higher flight of absiuxlity ; for, to refute tlie proposition, it is 
lirst falsely translated into nonsense. Its true meaning, both 
quantified terms being taken distributively, is : — All several men 
are some several animals, or, Every several man is some several 
animal. 

In these two cases, therefore, all is correct, and the objection 
from the identity or absurdity of a quantified predicate, null. 

Third Case. — " Sumatur signum subjecti distributive, signum 
prffidicati collective, sensus erit : Quoddam individuum animalis 
est U7iiversa species hon^inisy 

Fourth Case. — " Sumatur, denique, signum subjecti collective, 
signum j)r9edicati distributive, sensus erit : Quwdam species ani- 
malis, ut universale et ptrwdicabile, est omne individuum hominis." 

In regard to these last two cases, it is sufficient to refer to what 
lias been already said in answer to Ammonius (p. 296) ; or simj^ly 
to recall the postulate, that in the same logical unity (proposition 
or syllogism) the terms should be supposed in the same sense. If 
this postulate be obeyed, these two cases are inept, and, conse- 
quently, the objections superfluous. 

Ridiger then proceeds to treat us with four long " demonstra- 
tions a p7-iori,^' and to one elaborate " demonstration a posteriori ;" 
but as these are all founded on the blunders now exposed, it would 
be idle to refute them in detail. 

Ridiger, it m.ay well surprise us, howbeit the professed cham- 
pion of " the old and correct doctrine," is virtually, perhaps uncon- 
sciously, a confessor of the truth of " the new and false prejudice ; " 
for I find him propounding four several syllogistic forms, three of 
which are only valid through the universal quantification of the 
predicate in affirmatives, and two, (including the other one), 2:)roceed 
on a correct, though partial, view, opposed to that of the logicians, 
touching the conclusion of the Second Figure, (L. II. c. vi.) I 
shall insert the quantities, operative but not expressed. 

In the First Figure — " At, aut ego nihil video, aut lorge natu- 
rali or est hie processus : — Quoddam fluidum est [quoddam] leve; 
quoddam corpus est \ovine] fluidum ; ergo quoddam corpus est 
quoddam leve; quam si dicas, &c., (§ 34<). — Here the middle 



APPENDIX. 315 

term is, and must be, affirmatively distributed as predicate. 



In the Second Figure. — " Verbi gratia: — Quoddani ens est 
[omne^ ani7nal : omnis homo est [quoddani\ animal; ergo, ornnis 
homo est [quoddam] ens. Hsec conclusio verissima, &c." (§ 89.) 
In like manner the middle is here universally quantified in an 
affirmative, f'luiiiiin M,^.^^iB: r. 



The following, Eidiger (p. 330) gives, as "two new moods, 
which cannot be dispensed with." — "Quoddani animal est [oninis] 
homo ; mdliim hrutum est \tdlus^ homo ; ergo, quoddam animal 
7ion est [ullum] hrutum.'' Item : — Quoddam animal non est 
\idlus] homo ; omnis civis est [quidam] homo ; ergo, quoddam 
animal non est [ullus] civis." — In the first of these, the middle, 
as predicate, is affirmatively distributed ; and in both syllogisms, 
one conclusion, denied by the logicians, is asserted by Ridiger, 
although the other, which involves a predicate, particular and 
negative, is recognised by neither. 



X. — Godfrey Ploucquet. 

Godfrey Ploucquet, a philosopher of some account, Professor 
of Logic and Metaphysic in the University of Tubingen, by various 
writings, from the year 1759, endeavoured to advance the science 
of reasoning ; and his failure was perhaps owing more to the 
inadequacy and limitation of his doctrine, than to its positive 
error. To say nothing about his attempt to reduce Logic to a 
species of computation, in which his one-sided views came into 
confliction with the one-sided views of Lambert, he undoubtedly 
commenced auspiciously, on the principle of a quantified predicate. 
This, like a few preceding logicians, he certainly saw afforded a 
mean of simplifying the conversion of propositions ;« but he did 
not see that it could accomplish much more, if properly applied, 

o An extract from his Fundamcnta quantification of the predicate, will be 
PhllosopJiia' Speculative, 1759, contain- found in Mr Bayues' Essaij, p. 128. 
ing Ploucquet'i3 doctrine touching the 



31 G APPENDIX. 

in the theory of syllogism. On the contrary, in syllogistic, he pro- 
fessedly returns, on mature consideration, to the ordinary jjoint 
of view, and thinks himself successful in recalling the common 
doctrine of inference to a single canon. That canon is this : — 
" The terms in the conclusion are to be taken absolutely in the 
same extension which they hold in the antecedent." — " In conclusi- 
one sint termini jjlane iidem, qui in prtemissis, intuitu quantitatis." 
{Methodus tarn demonstrandi directe omnes syllogismorum 
species, quam vitia formce detegendi, ojye unius regidce; — Me- 
thodus calcvlandi in Logicis ; i^assiin. Both in 1763). This 
rule, as applied to his logical calculus, he thus enounces: "Arrange 
the terms in syllogistic order ; strike out the middle ; and the 
extremes then afford the conclusion." — " Deleatur in praemissis 
medius ; id quod restat indicat conclusionem." {Methodus calcu- 
landi, imssiin ; Elementa Philosopldce Contemplative^, Logica, 
§ 122, 1778.) This rule is simple enough, but, unfortimately, it is 
both inadequate and false Inadequate (and this was ahvays 
sufficiently apparent) ; for it does not enable us to ascertain, (and 
these the principal questions), how many terms, — of what identity 
• — of what quantity — and of what quality, can be legitimately 
jilaced in the antecedent. But it is not true, (though this was 
never signalised) ; for its peculiar principle is falsified by eight of 
the thirty-six moods, to wit, in affirmatives, by ix., x., xi., xii., and 
in negatives, by ix, b, x. a, xi. b, xii. a.a In all these, the quan- 
tity of an extreme in the conclusion is less than its quantity in the 
antecedent. We can hardly, therefore, wonder that Ploucquet's 
logical sj)eculations have been neglected or contemned ; although 
their author be an independent and learned thinker, and his works 
all well worthy of perusal. But, though dismissed by Hegel and 
other German logicians, not for its falsity, with sujireme contempt, 
Ploucquet's canon has, however, found its admirers in this country, 
where I have lately seen it promulgated as original. 

XI. — Uleich. 

Institutiones Logicce et Metaphysical, § 171, 1785. — "Non 

tantum subjecto ^ed et p7'cedicato, ad subjectum relato, sua constat 

quantitas, suumque igitur signum quantitatis prsefigere licet. Sed 

hgec prsedicati quantitas ex veterum prseceptis ssepe justo minor 

o See Table of Moods below. Appendix, XI. — Ed. 



APPENDIX. 317 

invenitur. In loco de conversione distinctius de eo exponetur." 
In that place, however, nothing of the kind appears.a 



IV. 

CANONS OF SYLLOGISM; GENEEAL HISTORICAL 
NOTICES AND CRITICISM. 

A. HISTOEICAL NOTICES. 
(a) QUOTATIONS FROM VAEIOUS LOGICIANS. 

(Collectecl and Translated Autumn 1844. See above, Vol. I. p. 303. — Ed.) 

I — David Derodon. 

David Derodon (who died at Geneva in 1664-, and had been 
previously Professor of Philosophy at Die, Orange and Nismes), 
was a logician of no little f;xme among the French Huguenots ; the 
study of his works was, (if I recollect aright), even formally recom- 
mended to the brethren of their communion, by one of the Galli- 
can Synods. " Either the Devil or Doctor Derodon," was long 

a [That the Extension of Predicate is pp. 158, 283. Scotus, In An. Prior. L. i. 

always reduced to Extension of Subject, qu. 4,f. 240 ; qu. 13, ff. 254'', 255* ; qu. 

i.e., is equivalent to it, see Purchot, 14, f. 256''; qu. 23,f. 273*. 
Jnstit. Phil., Logica, i. pp. 123, 125. For instances of Aristotle virtually 

Ttslcy, El&niens d'Ideoloffie, t. iii. Disc, using distributed predicate, see .4 n.Pos^ 

Prel., pp. 99, 100. Cronsaz, Logique, t. i.6,% I. Cf. Zabarella, cul he. Opera 

iii. p. 190. Derodon, Zo^/ca Restituta, Logica, p. 7^5. The sa.me, In An. Post. 

P. ii., c. v., art. 4, p. 224. Boethius, O^JO'ct, I. 2. Opera, p. 827, and De Quarto, 

p. 348, (see above, p. 306). Sergeant, Figura Sijllog. Op., -p. 123. The adding 

Method to Science, b. ii., less. i. p. 127. mark of universality to predicate is, 

Beneke, Lehrhuch der Logik, § 156, p. Aristotle says, " useless and impossible" 

100. Stattler, Logica, § 196. (An Prior., i. c. 27, § 9); yet see ii. c. 

That the Predicate has quantity ; and 22, §§7, 8 ; c. 23, §§ 4, 5. On this 

potential designation of it as well as question, see Bolzano, Logik, % 131, p. 

the Subject, see Hoffbauer, Analytih 27, (and above, pp. 295, 301, 302.) 
der Urtheile und Schliisse, § 31 e< seq. That the predesignation of the predi- 

Lambert, Deutsclier Gelehrter Prie/tcech- cate by all collectively, in fact, reduces 

sel, Brief vi. vol. i. p. 395. Platner, the univei'sal to a singular proposition, 

Philosophischc Aphorismen, i. § 546. see Purchot, Instit. Phil., i. p. 124. Cf. 

Corvinus, Instit. Phil. Pat., § 413. Logica Contractu Trajectina, P. ii. c. 5. 

Conimbricenses, In Ai'ist. Dial., t. ii. (1707.)] 



818 APPENDIX. 

a proverbial expression in France for tlie authorship of an acute 
argument ; and the " Sepulchre of the Mass" has been translated 
into the vernacular of every Calvinist country. Derodon has left 
two systems of Logic ; a larger, {Logica Restituta, 1659), and a 
smaller {Logica Contracta, 1664), both published in 4to.a I shall 
quote only from the former. 

It is impossible to deny Derodon's subtlety, but his blunders 
unfortunately outweigh his originality. Leaving Conversion as he 
found it, after reiDcating, with approbation, the old rules, — that the 
predicate is not to be overtly quantified universally, (p. 573), but 
to be taken, in affirmative propositions particularly, as in negative 
propositions universally, (p. 623) ; we are surprised to find him 
controverting, in detail, the special rules of syllogism. This polemic, 
as might be exj^ected, is signally unsuccessful ; for it is frequently 
at variance with all principle, and uniforndy in contradiction of his 
own. It is, indeed, only interesting as a manifestation, that the old 
logical doctrine was obscurely felt by so original a thinker to be 
erroneous ; for the corrections attempted by Derodon are, them- 
selves, especially on the ground which he adoj^ts, only so many 
errors. He unhappily starts with a blunder ; for he gives, as rectus, 
an examjile of syllogism, in which the middle term is, even of ne- 
cessity, undistributed ; and he goes on (pp. 627, 628, 636, 637, 638, 
639, 619) either to stumble in the same fashion, or to adduce rea- 
sonings, which can only be vindicated as inferential, by supplying 
a universal quantity to the predicate in affirmative propositions, 
or by reducing it to particularity in negatives ; both in the teeth 
of Derodon's own laws. I have, however, recorded, in my Table of 
Syllogisms, some of his examples, both the two forms which he has 
named, and four others which he only enounces ; according, by 
liberal construction, what was requisite to give them sense, and 
which, without doubt, the author would himself have recognised. 

II. — Eapin. 

Rapin, Reflexions sur la Logique, § 4, 1684. 

" Before Aristotle there had appeared nothing on logic systematic 

« Derodon seems wholly unknown to a considerable number in the .^amebind- 

the German logicians, and, I need hardly ing must have been imported at once, 

add, to those of other countries. In probably in consequence of the synodical 

Scotland his works are not of the rarest ; recommendation. 



APPENDIX. 819 

and established. His genius, so full of reason and intelligence, 
penetrated to the recesses of the mind of man, and laid open all 
its secret workings in the accurate analysis wMch he made of its 
operations. The depths of human thought had not as yet been 
fathomed. Aristotle was the first who discovered the new way 
of attaining to science, by the evidence of demonstration, and of 
proceeding geometrically to demonstration, by the infallibility of 
the syllogism, the most accomplished work and mightiest effort of 
the human mind," &c. 

Rapin errs in making Aristotle lay the rule of proportion along 
with the Dictum de Omni as a princijile of syllogism. 

Ill— Leibnitz. 

Leibnitz, De la confoi'mite de la Foi avec la Raison, § 22. 
Op. t. i., p. 81. " Hence the facility of some WTiters is too great, 
in conceding that the doctrine of the Holy Trinity is repugnant 
with that great principle which enounces — What ai'e the same 
with the same third, are the same with each other ; that is, if A 
be the same with B, and C be the same with B, it is necessary that 
A and C should also be the same with one another. For this 
principle flows immediately from the principle of Contradiction, 
and is the ground and basis of all Logic ; if that fail, there is no 
longer any way of reasoning with certainty." 

IV.— Reusch. 

Reusch, Sy sterna Logicum, 1734. 

§ 506. "That dictum of the Aristotelians de Omni et Kidlo, 
(503), evinces, indeed, a legitimate consequence, but it only regu- 
lates one species of syllogisms, at least immediately. By this reason, 
therefore, logicians have been induced to prove the consequence of 
the other sj)ecies by means of the first, to which they are reduced. 
But, that we may be able to supersede this labour, I have en- 
deavoured to give a broader basis to the Dictum de Omni et Nullo, 
or by whatever name that rule is called, to which, in the construc- 
tion of syllogisms, the order of thought is conformed. 

§ 507. " For the whole business of ordinary reasoning is accom- 
plished by the substitution of ideas in place of the subject or predi- 



320 APPENDIX. 

cate of the fundamental proposition. This some call the equation 
of thoughts. Now, the fundamental proposition may be either 
affirmative or negative, and in each the ideas of the terms may be 
considered either agreeing or diverse, and according to this various 
relation there obtains a various substitution, which we shall clearly 
illustrate before engaging with our doctrine of the Dictum de 
Omni et Nullo." [Having done this at great length, he proceeds]. 

§ "510. From what has been now fully declared, the following 
Dictum de Omni et Nullo may be formed, which the definition 
itself of reasoning and syllogism (§ 502) supports, and to which 
all syllogisms in every figure and mood may be accommodated. 

"If two ideas (two terms) have, through a judgment, (proposi- 
tion), received a relation to each other, either affirmative or nega- 
tive, in that case it is allowable, in place of either of these, (that 
is, the subject or predicate of that judgment or proposition), to sub- 
stitute another idea, (term), according to the rules given of Equi- 
poUence or Reciprocation (§ 508, s. 9), of Subordination, of Co- 
ordination," (see Waldin, below, p. 824!). 

IV.— Ceusius. 

Crusius, Weg zur Gewissheit. Ed. i. 1747; Ed. ii. 1762. 

§ 256. " The supreme law of all syllogism is. What we cannot 
otherwise think than as true, is true, and what we absolutely can- 
not think at all, or cannot think but as false, isfalse."^ 

§ 259. Of necessary judgments, of judgments which we cannot 
but think, " which are not identical, and which constitute, in the 
last result, the positive or the kernel in our knowledge ; to which 
we apply the principle of Contradiction, and thereby enrich the 



a Kant, {iiber die. Evidenz in mefa- if it be agreed that no other principle 
physischen Wissenschaftcn, 1763, Verm, of truth is possible than inasmuch as 
Schrift. ii. 43), has hereon the following we are incapable of holding a thing not 
observation : — "In regard to the su- for true, in this case it is acknowledged 
preme rule of all certainty which this that no other principle of truth is corn- 
celebrated man thought of placing as petent, and that knowledge is indemon- 
the principle of all knowledge, and, strable. It is indeed true that there are 
consequently, also of the metaphysical, many indemonstrable knowledges, but 

What I cannot otherwise think than as the feeling of conviction in regard to 

true is true, &c. ; it is manifest that this them is a confession, but not a ground 

proposition can never be a principle of of proof, that they are true." — See also 

truth for any knowledge whatever. For Reid, Inlellcctual Powers, Esmy iv. ch. 4. 



APPENDIX. 321 

understanding with a knowledge of real judgments," — such judg- 
ments are principally the following : Every power or force is in- 
herent in a subject ; All that ai^ises, (begins to be), arises in virtue 
of a suffi^cient cause; All whose non-existence cannot be thought, 
has its cause, and has at some time arisen, (begun to be) ; Evei^ 
substance exists somewhere ; All that exists, exists at some time; 
Two7naterial things cannot exist at the same time,and in jprecisely 
the same j^lace. There are also many other propositions, which 
treat of the determinate qualification of things as present ; for ex- 
ample — The same point of a body cannot be at once red and green ; 
A man cannot be in two places at once, and so forth. 

" § 261. All the judgments previously alleged, (§ 259), may be 
comprehended under these two general propositions, — What can- 
not in thought be separated from each other, cannot be separated 
from each other in reality ; and, What cannot in thought be con- 
nected into a notion, cannot in reality be connected; to vAi, 
although no contradiction shows itself between the notions, but we 
are only conscious of a j)hysical necessity to think the thing so and 
so, clearly and after a comparison of all the circumstances with 
each other. For we now speak of jiropositions which are not 
identical with the Principle of Contradiction, but of such as prima- 
rily afford the matters on which it may be applied. Hence we see 
that the supreme principle of our knowledge given above, (§ 256), 
has two determinations ; inasmuch as the impossibility to think a 
something arises, either because a contradiction would ensue, or 
because we are positively so compelled by the physical constitution 
of our thinking faculties. 

"§ 262. The highest principle of all syllogism thus resolves itself 
into the three caj^ital propositions ; 

1. Nothing can at once be and not be in the same j^oint of view. 

2. Things which cannot be thought without each other, without 
each other cannot exist. 

3. What cannot be thought as with and beside each other, can- 
not exist with and beside each other, on the supposition even that 
between the notions there is no contradiction. 

"The second of these capital propositions I call the Principle 
of Inseparables, {principiuni inseparabilium) ; and the third 
the Principle of Inconjoinables, {principium inconjungibilium). 
They may be also termed the three Pj^inciples of Reason. 

VOL. II. X 



II 



322 APPENDIX. 

Cli. VIII. Of the different sjiecies of syllogisms, he says, (§ 272), 
"among the higher principles of syllogisms it is needful only 
to enumerate the Principle of Contradiction, and the Principle 
of Su^cient Reason, w\\\c\\ is subsumed from the principle of In- 
separables, (§ 262). We shall state the laws of syllogism in this 
order, — Consider those which flow, 1°, Prom the Principle of 
Contradiction ; 2°, Erom the Principle of Sufficient Reason ; and, 
3°, From both together." 

V. — Francis Hutcheson. 

[Francisci Hutcheson.] Logicm Compendium. Glasguce, in 
wdibus academicis, excudebant Rohertus et Andreas Foidis, Aca- 
demice Typograplii. 1764. 

Part III., Ch. ii.. p. 58. 

" The whole force of syllogism may be explicated from the fol- 
lowing axioms. 

" First Axiom. — Things which agree in the same third, agree 
among themselves. 

" Second Axiom. — Things whereof the one agrees, the other 
does not agr-ee, in one and the same thij-d, these things do not 
agree among themselves. 

" Third Axiom. — Things which agree in no tliird, do not agree 
among themselves. 

Fourth Axiom. — Things which disagree in no third, do not 
disagree among themselves!' 

" Hence are deduced the general rules of syllogisms. 

"Of these the three first regard the Quality [not alone] of Pro- 
positions. 

" Rule 1. — If one of the premises he negative, the conclusion 
will he negative (by Ax. 2). 

"Rule 2. If hoth premises he affirmative, the conclusion will he 
affrmative (by Ax. 1). 

" Rule 3. — If hoth premises he negative, nothing follows : because 
of things mutually agreeing and mutually disagreeing, both may 
be different from a third thing (by Ax. 3, 4). 

" Two Rules regard the Quantity of Terms. 

" Rule 4. — Let the middle he once at least distributed, or taken 



APPENDIX. 323 

universally ; for the common term frequently contains two or more 
species mutually opposed, of which it may be predicated according 
to various parts of its extension ; these [specific] terms do not, 
therefore, truly agree in one third, unless one at least of them 
agrees with the whole middle (by Ax. 3, 4). 

" Eule 5. — No term ought to he taken more universally in the 
conclusion than in the premises : because no consequence is valid 
from the particular to the universal. [Because we should, in that 
case, transcend the agreement or disagreement of the two terms 
in a third, on which, ex hypothesi, we found]. 

" [In like manner there are two rules] concerning the Quantity 
of Propositions. 

"Rule 6. — If one of the premises he particular^ the conclusion 
will also he particular. 

" Por, Case I. — If the conclusion be affirmative, therefore both 
premises will be affirmative (by Rule 1). But, in a particular pro- 
position, there is no term distributed ; the middle is, therefore, to 
be distributed in one or other of the premises (by Rule 4). It will, 
therefore, be the subject of a universal affirmative proposition ; 
but the other extreme is also taken particularly, when it is the 
predicate of an affirmative proposition, the conclusion will, there- 
fore, be particular (by Rule 5). 

" Case 2. — Let the conclusion be negative ; its jDredicate is, 
therefore, distributed : hence, in the premises, the major and the 
middle terms are to be distributed (by Rules 5 and 4). 

" But when one of the premises is negative, the other is affirma- 
tive (by Rule 3). If one premise be particular, these two terms only 
can be distributed ; since one premise affirms, whilst the other is 
particular. The minor extreme, the subject of the conclusion, is 
not, therefore, distributed in the premises ; it cannot, therefore, (by 
Rule 5), be distributed in the conclusion. 

"Rule?. — From two particular premises nothing folloius ; at 
least according to the accustomed mode of speaking, where the pre- 
dicate of a negative proposition is understood to be distributed. 
For, l"". If the conclusion affirm, both premises will affirm, and, 
consequently, no term is distributed in the premises ; contrary to 
^ule 4. 2°, Let the conclusion be negative, its predicate is there- 
fore distributed ; but in particular premises there is only distributed 



324 



APPENDIX. 



the predicate of a negative proposition ; there is, therefore, neces- 
sarily a vice, (either against Kule 4 or Rule 5)." a 

VI. — Savonaeola. 

Savonarola, Compendium Logices, L. iv. p. 115, ed. Venetiis, 
1542. — " In whatever syllogism any j^roposition can be concluded, 
there may also be concluded every other proposition which follows 
out from it." On this he remarks : "When any syllogism infers a 
conclusion flowing from its immediate conclusion, it is not to be 
called one syllogism but two. For that other conclusion does not 
follow simply in virtue of the premises, but in virtue of them 
there first follows the proper conclusion, and from this conclusion 
there follows, by another syllogism, the conclusion consequent on it. 
Hence there are tacitly two syllogisms ; otherwise the moods of 
syllogisms would be almost infinite." 



VII. — Baumgarten. 

Baumgarten, Acroasis Logica. Ed. Tollner. Ed. I. 1765, 
§ 297. " Every reasoning depends on this proposition : — A and 
B connected with a third C, are connected with each other : in 
affirmation immediately, in negation mediately. This proposition 
is, therefore, the foundation and principle of all reasoning ; which, 
however, is subordinate to the principle of Contradiction. 

§ 824. " Every ordinary syllogism concluding according to the 



a " Rules 1 and 7 are thus contracted 
into one : The conclusion follows the 
weaker j)art ; that is, the negative or 
the particular. All these Rules are in- 
cluded in the following verses : 

Distribuas medium, nee quartus ter- 
minus adsit, 
Utraque nee prtemissa negans, nee 

particularis. 
Sectetur partem conclusio deterio- 

rem ; 
Et non distribuat nisi cum in-cemissa, 
negetve. 
In an unusual mode of speaking, a cer- 
tain negative conclusion may be effected 
with a non-distributive predicate. As 
in this exam file 



A B 

Some Frenchmen are [some] learned ; 

C B 

Some Englishmen are not [any] learned, 
Therefore, some Englishmen are not some 
Frenchmen." 




(What are within [ ] are by me). 
[Written Autumn 1844. In the latest 
notation (,) is substituted for (.), and (:) 
for (:.). See below, Appendix XI. — Ed] 



APPENDIX. 325 

Dictum, either de Omni, or de Nidlo. This Dictum is thus the 
foundation of all ordinary syllogisms," (It had been previously 
announced, §§ 319, 321.) 

"Whatever is truly affirmed of a notion universally, is also truly 
affirmed of all that is contained under it. Whatever is truly 
denied of a notion universally, is also truly denied of all that is 
contained under it." 

VIII.— Eeimaeus. 

Eeimarus, Vernunftlehre. 1766. 

§ 176. " The fundamental rules of syllogism are, consequently, 
no other than the rules of Agreement [Identity] and of Contradic- 
tion. For what the geometer in regard to magnitudes takes as 
the rule of equality or inequality, that the reasoner here adopts as 
the universal rule of all mediate insight : — If two things he iden- 
tical with a third, they are also in so far identical with each 
other. But if the one he, and the other he not, identical with the 
third, then they are not 'mutually identical, hut rather mutually 
repugnant." 

§ 177. Here he notices that the Dictum de Omni et Nullo is 
not properly a rule for all figures, but for the first alone, 

IX. — Waldin, 

Waldin, Novum Logicce Systema. 1766. 

§ 335. " Since the syllogism requires essentially nothing but a 
distinct cognition of the sufficient reason of some proposition, the 
most universal rule of all syllogisms is, — Tlie sufficient reason of a 
given proposition is to he distinctly cognised. 

§ 364. " The most general rule of all reasonings, (§ 335), remains 
also the rule of all reasonings as well in synthesis as in analysis. 
But in the synthesis of the ordinary syllogism, the middle term in 
the major proposition is referred to the major term, in the minor 
proposition to the mmor term. (§ 360). Wherefore, from this 
relation we must judge whether the middle term be or be not the 
sufficient reason of the conclusion. Wherefore, the synthesis of the 
ordinary syllogism is to be cognised from the relation of its ideas. 
This you may thus express : 

" 1,) After the true projwsition, the relation of whose ex- 
tremes you distinctly apprehend ; 



326 APPENDIX. 

" 2.) Add to its subject or iDvedicate another idea different 
from both, whether agreeing or disagreeing ; 

" 3.) Inquire into the relation of the added idea, to the end 
that you mau knoiv whether the middle term in the given relation 
infer the conclusion; and this is known by tlie application of the 
rules of Reciprocation, Subordination, Go-ordination, and Oppo- 
sition. If any one wish to call this the Dictum de Omni et Nullo, 
I have no objections." 

" Observation. This they call the Dictum de Omni et Nullo of 
the celebrated Rensch. It stands true indeed ; but is beset with diffi- 
culties, inasmuch as it is rather a complesus of all rules than one 
only, which as yet is to be referred to the class of pia desideria. 
Logicians have, indeed, taken pains to discover one supreme rule 
of all ordinary reasonings ; but no one has as yet been so happy 
as to find it out." Then follows a criticism of the attempts by the 
Port Royal and Syrbius. 

X. — Stattlee. 

Stattler, Philosophia, P. I, Logica, 1769. 

§ 237. " In this comparison of two ideas with a third, six 
different cases may in all occur : for either, 

1.) " One of the two ideas contains that same third, which 
again contains the other ; or, 

2.) " Both of the two are contained in the third ; or, 

3.) " Each of the two contains the third ; or, 

4.) " One of the two contains the third, the other being repug- 
nant with it ; or, 

5.) " One of the two is contained in the third, luith luhich the 
other is repugnant ; or, 

6.) Both of the two are repugnant to the third. 

" The former three cases generate an affirmative conclusion, the 
latter three a negative." In a note Stattler eliminates a seventh case, 
in which neither may contain, and neither be repugnant to the 
third. 

§ 244. General Law of all Reasonings. '' In all reasonings, 
as often as a consequent is, by legitimate form, inferred from 
an antecedent, so often is there included in the antecedent what 
the consequent enounces ; cither the congruity and reciprocal 



APPENDIX. 827 

containment, or the 7'epugnance of A and 0; and if such be not 
included in one or other of the antecedents, whatever is inferred 
in the consequent is void of legitimate form." 

XI. — SautePw 

Sauter, Institutiones Logicce, 1798. 

§ 123. " Foundatiojis of Syllogism. — In every syllogism there 
are two notions compared with a third, to the end that it may 
appear whether they are to be conjoined or sejoined. There are, 
therefore, here, three possible cases. For there agree with the 
assumed third, either both notions, or one, or neither. In reasoning, 
our mind, therefore, reposes on these axioms, as on fundamental 
principles. 

].) " Wliere two notions agree with the same third, they agree 
with one anotJter. 

2.) " Where one is contained by the third, luith luhich the other 
is repugnantj they are mutually repugnant. 

3.) " When neither notions agrees with the third, there is between 
them neither agreement nor repugnance." 

XII. — SUTER. 
Suter, Logica. 

§ 61. " Quae eidem tertio conveniunt vel disconveniunt, etiam 
conveniunt vel disconveniunt inter se." 

XIII.— Seguy. 

Seguy, Philosophia ad Usum Scholarum Accommodata, T. I. 
Logica. Paris, 1771. 

P. 175, ed. 1785. " Concerning the rule of recent philoso- 
phers." 

Having recited the general rule of the Port Royal Logic, he 
thus comments on it : — 

" 1°, This is nothing else than the principle of reasoning ; there- 
fore, it is improperly adduced as a new discovery, or a rule strictly 
so called. 

" 2°, It may be useful, to the rude and inexperienced, to recog- 
nise whether a syllogism be legitimate or illicit. 

" But the principal fault of this rule is, that it contains no certain 
method whereby we may know when, and when not, one of the 



328 APPENDIX. 

premises contains a conclusion ; for the discovery of which we 
must frequently recur to the general rules."" 

P. 178. Seguy exposes Father Buffier's error in saying "that, 
according to Aristotle and the common rules of Logic, the middle 
term ought absolutely to be the predicate in the first or major 
proposition ;" seeing that the middle term is not the predicate in 
the first and third Figures. This must be a mistake ; for I can- 
not find such a doctrine in Buffier, who in this respect, in many 
places, teaches the correct. 



XI v.— HOFFBAUEE. 

Hoffbauer, Anfangsgrilnde der Logik, ITO^, 1810. 

"§317. Fundamental Principles. 

" I. 1.) An attribute which belongs to all and every of the objects 
contained under a notion, may also be aflSrmed of these objects so 
contained. (Dictum de Omni.) 

" 2.) An attribute which belongs to none of the objects contained 
under a notion, must also be denied of these objects so contained. 
(Dictum de Nulla) 

" II. When, of the objects X and Z, the one contains an atttri- 
bute which the other does not contain, and they are thus different 
from each other, then X is not Z, and Z is not X. 

" III. 1.) When objects which are contained under a notion a are 
also contained under another notion h, then this last notion con- 
tains under it some at least of the objects which are contained 
under the first. 

" 2.) If certain objects which are not contained under a notion a 
are contained under h, then 6 contains under it some at least of 
the objects which are not contained under a. 

" IV. 1.) If objects which are contained under a notion a belong 

o Followed by Tjarroque, Elemens de E contra, PhilosopJiia Lugdunensis, i. 
Philosophie, p. 231 ; Galluppi, Ze2/or^^ rfj 159. Troxler, Logik,\l 41. 
Logica e di Metafisica, 1. 47, i. 348. 



APPENDIX. 329 

to those which are contained under another notion h, tlien this 
second notion b contains under it some at least of the objects 
which are contained under a. 

" 2.) If all objects which are contained under a notion a belong 
to those which are not contained under a certain other notioii b, 
then this notion b contains under it no object w^hich is contained 
under the notion a. 

" 3.) If all the objects contained under a certain notion a are 
different from certain other objects contained under b, then b con- 
tains under it at least some objects which are not contained 
under a. 

XV.— Kant. 

Kant, Logik 1800-6. II. Syllogisms. 

" § 56. Syllogism in general. — A syllogism is the cognition that 
a certain proposition is necessary, through the subsumption of its 
condition under a given general rule. 

" § 57. General principle of all Syllogisms. — The general 
principle whereon the validity of all inference, through the 
reason, rests, may be determinately enounced in the following 
formula : — 

" What stands under the condition of a rule, that stands also 
under the rule itself 

" Observation. — The syllogism premises a General Ride, and a 
Sid)Sumption under its Condition. Hereby we understand the con- 
clusion a priori, not as manifested in things individual, but as 
universally maintained, and as necessary under a certain condition. 
And this, that all stands under the universal, and is determinable 
in universal laws, is the Principle HhqM oi Rationality ov oi Neces- 
sity, (principium rationalitatis sen necessitatis) 

" § 58. Essential constituents of the Syllogism. — To every syl- 
logism there belong the three following parts : — 

"1.) A general rule, styled ih^Q Major proposition, (pivjwsitio 
major, Obersatz) 

" 2.) The proposition which subsumes a cognition under the con- 
dition of the general rule, called the Minor proposition, {propositio 
minor, Untersatz) ; and, finally, 

" 8.) The proposition which affirms or denies the predicate in the 



330 APPENDIX. 

rule of the subsumed cognition, — the Concluding proposition,, or 
Conclusion, {Gonclusio, tichlasssatz). 

" The two first propositions, taken in connection with each other, 
are called the Antecedents, or Premises, ( Voi'dersdtze). 

" Observation. — A rule is the assertion of a general condition. 
The relation of the condition to the assertion, how, to wit, this 
stands under that, is the Exponent of the rule. The cognition, 
that the condition, (somewhere or other), takes place, is the Suh- 
sumption. 

" The nexus of what is subsumed under the condition, with the 
assertion of the rule, is the Conclusion." 

Having shown the distribution of syllogisms into Categorical, 
Hypothetical, and Disjunctive, he proceeds to speak of the first 
class. 

" § 63. Principle of Categorical Syllogisms. — The principle 
whereon the possibility and validity of Categorical Syllogisms 
is this, — ^What pertains to the attribute of a thing, that pertains to 
the thing itself ; and what is repugnant to the attribute of a thing, 
that is repugnant to the thing itself, {Nota notce est nota rei ipsius; 
Repugnans notce, repugnat rei ipsi). 

" Observation. — From this principle, the so-called Dictum de Omni 
et Nullo is easily deduced, and cannot, therefore, be regarded as the 
highest principle either of the Syllogism in general, or of the Cate- 
gorical Syllogism in particular. Ge7ieric and Specific Notions are 
in fact the general notes or attributes of all the things which stand 
under these notions. Consequently the rule is here valid — What 
pertains or is repugnant to the genus or species, that also per- 
tains or is repugnant to all the objects which are contained 
under that genus or species. And this very ride it is which is 
called the Dictum de Omni et Nullo." 

XVI.— Cheistian Weiss. 

Christian Weiss, Logik, 1801. 

"§ 216. Principle for all Syllogisms. — The principle of every 
perfect Syllogism consists in the relation of one of the notions 
contained in the conclusion to a third notion [terminus medius), 
to which the other notion of the conclusion belongs. Noiu the re- 
lation ivhich tJte first of these holds to the middle notion, the 



APPENDIX. 831 

same r>iust hold to the second, just because the second coin- 
cides with the middle notion to the same extent as the first. 

'-' Remark. — 'Relation to' means only any determinately 
thought relation, expressed in a judgment 

" The older logicians adopt, some of them, the principle Nota 
notcB est notarei ipsius, — quod rejjugnat notes, repugned ipsirei ; 
this, however, is only properly applicable to the first figure. The 
expression of others is preferable, Queecumque conveniunt {vet 
dissentiunt) in uno tertio, eadem conveniun (vel dissentiunt) inter 
se. Others, in fine, among whom is Wolf, give the Dictum de 
Omni et Nullo (cf § 233) as the princij)le of syllogisms in gene- 
ral ; compare Philosophical Aphorisms [of Platner], P, i. § 54^6. 
All inference takes place according to a universal rule of reason, 
here only expressed in reference to syllogism, to which, however, 
some have chosen to give a more mathematical expression ; — If 
two notions be equed to a third, they arc also equed to eeich other. 

[]\^ota bene. — Weiss's mistake (§ 231) in supposing that Aris- 
totle " designated the syllogistic moods with words, like his learned 
followers."] 

" § 231. Categorical Syllogisms, Figure I. — The first figure con- 
cludes by means of a subordination of the minor term in the 
conclusion under the subject of another judgment. 

" § 233. This takes place under the general principle : — 

" 1.) What pertains to edl objects conteiined under a notion, 
that pertains edso to some and to each individual of their num- 
ber among them. 

"2.) What belongs to none of the objects contained under a 
notion, that also does not pertain to some or to any individual of 
their number among them. 

" These are the celebrated Dicta de Omni and de Nidlo, — Quid- 
quid preedicatur de onini, idem etiam de ediquo, and, Quielquid 
prcedicatur de nullo, id nee de cdiequo proedicatur." 

XVII.— Fries. 

Fries, System der Logik. 

" § 52. Hitherto we have maintained two views of the Syllogism 
in connection. The end in view of reasoning is this, — that cases 
should be subordinated to general rules, and through them become 
determined. For example, the general law of the mutual attrac- 



332 APPENDIX. 

tion of all heavenly bodies has its Avhole significance, for my 
knowledge, in this, that there are given individnal heavenly 
bodies, as Sun and Earth, to which I apply it. To enoimce these 
relations, it is, in the first place, necessary that I have a general rule, 
as Major Proposition, (Obersatz) ; in the second, a Minor Propo- 
sition, (Untersatz), which subordinates cases to the rule, and, 
finally, a Concluding Proposition, which determines the cases 
through the rule. On the other hand, we see that every Con- 
clusion is an analytico-hypothetic judgment, and this always 
flows from the Dictum de Omni et Nullo, inasmuch as the relation 
of subordination of particular under universal notions, is the only 
relation of Reason and Consequent given in the form of thought 
itself. Now, if the conclusion, as syllogism, combines a plurality 
of judgments in its premises, in this case the principle of the in- 
ference must lie in a connection of the thoughts, — a connection 
which is determined by the matter of these judgments. In the 
simplest case, when taking into account only a single syllogism, 
I thus would recognise in the premises the relation of subordina- 
tion between two notions by reference to the same third notion, 
and therethrough jjcrceive in the conclusion the relation of these 
two notions to each other. I know, for example, that all men 
are infiortal, and that Gains is a man. Consequently, through the 
relation of the notion of moi^tality, and of my imagination of 
Caius, to the notion man, the relation of Caius to mortaliti/ is 
likewise determined : — Caius is mortal. The first of these views 
is a mere postulate ; but in conformity to the second we are 
enabled immediately to evolve the general form of syllogisms, and 
from this evolution does it then become manifest that all possible 
syllogisms satisfy the postulate. We, therefore, in the first instance, 
attach ourselves to the second view. Through this there is deter- 
mined as follows : — 

" 1.) Here the determination of one notion is carried over to an- 
other, superordinate or subordinate to itself. To every syllogism 
there belong three notions, called its tei'ms, (termini). (We say 
notions, (Begriffe), because they are, in general, such, and when indi- 
vidual representations [or images] appear as terms, in that case 
there is no inter- commutation possible). A major term, or supe- 
rior notion, {Oberhegriff), P, is given as the logical determination 
of a middle term or notion, (Mittelbegriff), M, and, through this, 



APPENDIX. 333 

it is positively or negatively stated as the determination of a minor 
term or notion, {Unterhegriff), S. 

" 2.) If, then, we regard the propositions in which these relations 
are enounced ; there is, firstly, in the conclusion, [Schlusssatz], 
the minor term, or inferior notion, subordinated to the major term, 
or superior notion, (S is P). Further, in one of the premises, the 
middle must be connected with the major term or notion, (M is P). 
This is called the major proposition, {Ohei^satz). In the other, 
again, the minor is connected with the major term or notion, (S is 
M) ; this is called the minor 2')roposition, {Untersatz). 

"The form of every syllogism is therefore : — 

Major Proposition, M is P. 

Minor Proposition, S is M. 



Conclusion, S is P. 

" In the example given above, man is the middle term ; moHality 
the major term ; and Caius the minor term. The syllogism is : — 

Major Proposition, All men are mortal ; 

Minor Proposition, Caius is a man ; 



Conclusion, Caius is mortal. 

" The fundamental relation in all syllogisms is that of the 
middle term to the major and minor terms, in other words, that of 
the carrying over of a logical determination from one notion to 
another, through certain given subordinations. Tor howbeit the 
Dictum de Omni et Nullo, as a common principle of all syllogisms 
in the formula, — What liolds good of the universal, holds also good 
of the particulars subordinate thereto, and still more in that 
other, — The attribute of the atti^ibute is also the attribute of the 
thing itself, — is proximately only applicable to the categorical sub- 
ordination of a representation [or notion] under a notion ; stiU, 
however, the law of mental connection is altogether the same in 
syllogisms determined by the subordination of consequence under 
a reason, [Hypothetic Syllogisms], or of the complement of parts 
under a logical whole, [Disjunctive Syllogisms]. The displayed 
form is the form of every possible syllogism. In fact, it also coin- 



334 APPENDIX. 

cides with the first requirement that, in the syllogism, a case 
should always be determined by a rule, inasmuch as every syllo- 
gism proposes a universal premise, in order rigorously to infer its 
conclusion. This will be more definitely shown, when we treat of 
syllogisms in detail. Only the declaration, tliat the rule is always 
the major 'proposition, is sometimes at variance with the declara- 
tion, that the major proposition contains the relation of the 
middle term to the major term. We must, however, in the first 
place, always follow the determination of the latter. For every 
syllogism properly contains the three processes: — 1). The subor- 
dination of a particular under a universal ; this is the function of 
the minor proposition, and the relation between the minor and major 
terms ; 2), Postulate of a logical determination for one of these 
two ; this is the function of the major jjroposition, and the relation 
of the middle to the major term ; 3), The carrying over this deter- 
mination to that other ; this is the function of the conclusion and 
the relation of the minor to the major term. 

" § 53. The subordination of a particular to a universal must, 
therefore, in every syllogism, be understood wholly in general. 
Here either a particular may be determined through its superordi- 
nated universal, and such an inference from universal to particular 
we shall call a syllogism in the first figure ; or there is a universal 
known through its subordinated particular, and this inference from 
the particular to the universal is called a syllogism in the second 
\third^ figure. If, for example, the subordination is given me, — 
A II gold is metal ; I can either transfer an attribute of metal, 
for instance fusibility, to the gold, or enounce an attribute of 
gold, ductility, for instance, of some metal. In the first case, I 
draw a conclusion in the first figure, from the universal to the 

particular : — 

A II metal is fusible ; 
All gold is metal ; 

All gold is fusible. 

" In the other case, I conclude in the second [third] figure from 
the particular to the general : — 

All gold is ductile ; 
A II gold is metal ; 

Some Tnetal is dtictile." 



APPENDIX. 835 

Then, after distribution of the Syllogism into Categorical, Hypo- 
thetical, and Divisive, (Disjunctive), he proceeds with the first 
class. 

XVIII. — KlESEWETTER. 

Kiesewetter, AUgemeine Logik, 1801, 1824*. I. Theil. 

"§ 228. — All pure Categorical Syllogisms, whose conclusion is an 
affirmative judgment, rest on the following principle : — What j^ei-- 
tains to the attribute of an object, j^ertains to the object itself. All 
syllogisms, whose conclusion is a negative judgment, are based upon 
the principle : — What is repugnant to the attributes of an object, 
is repugnant to the object itself. Two principles which can be 
easily deduced, — the first from the principle of Identity, the second 
from the principle of Contradiction. 

" § 229. — If we take into consideration that the major proposi- 
tion of every categorical syllogism must be a universal rule, — from 
this there flow the following rules : — 

"1. Whatever is universally affirmed of a notion, that is also 
affirmed of everything contained under it. The Dictum de Omni. 

" 2. Wliat is universally denied of a notion is denied also of every- 
thing contained under it. The Dictum de Nullo. 

" These rules are also thus exj)ressed : — 

" What pertains to the genus or species, j)ertains also to whatever 
is contained under them. What is repugnant to the genus or 
species, is repugnant also to whatever is contained under them." 

See also the Weitere Auseinandersetzung on the paragraphs, 

XIX. — Laeroque. 

Larroque, EUmens de Philosophic, Paris, 1830. Logique, 
Ch. i., p. 202. " The attribute of an affirmative proposition is 
taken sometimes particularly, sometimes universally. It is taken 
particularly, when it has a greater extension than the subject ; uni- 
versally, when it has not a greater extension, which occurs in every 
proposition where the two terms are identical. The reason of this 
diff'erence is palpable. If the attribute be a term more general 
than the subject, we affirm that the subject is a species or indivi- 
dual contained in the extension of the attribute : — Man is mortal ; 
Paul is learned : — that is, man is one, and not the only, species 



S36 APPENDIX. 

contained in the extension of the term mortal ; Paul is an indivi- 
dual, and not every individual, contained in the extension of the 
term learned. If, on the contrary, the attribute be not more 
general than the subject, the attribute is the same thing with the 
subject, and, consequently, we affirm that the subject is all that is 
contained in the extension of the attribute : — A circle is a plane 
surface, which has all the points, in [a line called] its circumfer- 
ence, at an equal distance from a j)oint called its centre — that is, 
a circle is all or every plane surface, &c. 

" The attribute of a negative proposition is always taken univer- 
sally. When we deny an attribute of a subject, we deny of this 
subject everything that has the nature of that attribute, that is to 
say, all the species, as all the individuals, contained in its extension : 
The soul is not extended ; to wit the soul is not any of the species, 
not any of the individuals contained in the extension of the term 
extended." 

Ch. ii., p. 230. "We have supposed, in the demonstration of 
these rules [the general rules of the Categorical Syllogism], that 
the attribute of an affirmative premise is always taken particularly. 
It would, therefore, seem that the calculations on which this demon- 
stration rests, are erroneous, whensoever the attribute is not a term 
more general than the subject, for we have seen that, in these cases, 
the attribute can be taken universally. But it is to be observed, tliat 
when the two terms of a proposition are identical, if the one or the 
other may be taken universally, they cannot both be so taken at 
once ; and that, if it be the attribute which is taken universally, it 
ought to be substituted for the subject, which then affords a parti- 
cular attribute. A triangle is a figure which has three sides and 
three angles. We cannot say, A II triangle is all figure, which, &c. ; 
but we can say, A II triangle is some figure, which, &c. ; or, A II figure 
which has three sides and three angles, is some triangle. Now, in 
adopting either of these last expressions of the proposition, the 
attribute is particular." 

Ch. ii., p. 231. "We have seen that the Syllogism inferred from 
its premises a proposition to be proved ; now this conclusion can- 
not be inferred from, unless it be contained in, the premises. From 
this incontestable observation, the author of the Port Eoyal Logic 



APPENDIX. 837 

has endeavoured to draw the following pretended rule, by aid of 
which we may detect the vice of any fallacious reasoning whatso- 
ever : Thus, should one of the premises contain the conclusion^ 
and the other shoiu that it is so contained. A great many treatises 
on Logic call this the single ride of the moderns. This pompous 
denomination seems to point at some marvellous discovery, of 
which the ancients had no conception, — at some consummative 
result of the efforts of the human intellect. It is true, indeed, that 
a syllogism is invalid, if the conclusion be not contained in the 
premises ; but a fine discovery forsooth ! This all the world 
already knew, — Aristotle among the rest ; but he justly noted that 
it is not always easy to see whether the conclusion be contained 
in the premises, and it is to assure ourselves of this that he laid 
down his rules. The pretended rule of the Port Royal is, therefore, 
not one at all ; it enounces only an observation, true but barren." 

XX. — Galluppi. 

Galluppi, Lezioni di Logica e di Metajisica. 1832. Lez. 
xlvii., p. 353, ed. 1841. 

" In a reasoning there must be an idea, common to the two pre- 
mises ; and a judgment which affirms the identity, either partial 
or perfect, of the other two ideas." 

In the same Lecture, (p. 348), he shows that he is ignorant of the 
law quoted from the Philosophia Lugdunensis, being by the 
authors of the L'Art de Penser. 

XXI. — BUFFIER. 

Buffier, Premiere Logique, about 1725. The following is from 
the Recapitulation, § 1 09 : — 

The Syllogism is defined, a tissue of three propositions so con- 
stituted, that if the two former be true, it is impossible but that 
the third should be true also. (§ 62.) 

The first Proposition is called the Major ; the second the 
Minor ; the third the Conclusion, which last is the essential end 
in view of the syllogism. (§ 65.) 

Its art consists in causing a consciousness, that in the conclusion 
the idea of the subject comprises the idea of the predicate ; and 
this is done by means of a third idea, called the Middle Term, 
(because it is intermediate between the subject and predicate), in 

VOL. II. Y 



838 APPENDIX. 

such sort that it is comprised in the subject, and comprises the pre- 
dicate. (§ 67.) 

If the first thing comprise a second, in which a third is comprised, 
the first comprises the third. If a fluid comprise chocolate, in 
which cocoa is comprised, the fluid itself comprises cocoa. (§ 68.) 

To reach distant conclusions, there is required a plurality of 
syllogisms. (§ 71.) 

Our rule of itself suffices for all syllogisms ; even for the nega- 
tive ; for every negative syllogism is equivalent to an affirmative. 
(§77.) 

Hypothetical syllogisms consist in the enouncement by the 
major premise, that a proposition is true, in case there be found a 
certain condition ; and the minor premise shows that this condition 
is actually found. (§ 79.) 

Disjunctive syllogisms, to admit of an easy verification, ought to 
be reduced to hypotheticals. (§ 81.) 

Although the single rule, which is proposed for all syllogisms, be 
subject to certain changes of expression, it is nevertheless always 
the most easy ; in fact, all logical laws necessarily suppose this 
condition. (§ 87.) 

The employment of Grammar is essential for the practice of 
Logic. (§ 90.) 

By means of such practice, which enables us to estimate accu- 
rately the value of the terms in every proposition, we shall likewise 
obtain the rule for the discovery of all sophisms, which consist only 
of the mere equivocation of words, and of the ambiguity of propo- 
sitions. (§ 92 et seq.) 

XXII.— VlCTORIN. 

Victorin, Keue naturlichere Darstellung der Lo<jik,Yienvia.,18S5. 

II. Simple Categorical Syllogisms. § 04. The fundamental rule 
of all such syllogisms : — 

" In what relation a concept stands to one of two reci- 
procally subordinate concepts, in the same relation does it 
stand to the other." 

§ 91^. First Figure ; fundamental rule : — " As a notion deter- 
7nines the higher notion, so does it determine the lower of the 
same ;" or, " In tuhat relation a notion stands to one notion, in 
the same relation it stands to the loiuer of the same." 



APPENDIX. 339 

§ 96. Second Figure ; fundamental rule : — " Whentiuo notions 
are ojypositely determined hy a third notion, they are also them- 
selves opposed ;" or, " If two notions stand to a third in op- 
posed relations, they also themselves stand in a relation of 
opposition." 

§ 98. Third Figure ; fundamental rule : — " As a notion deter- 
mines the one of two [^o lY] subordinate notions, so does it de- 
termine the other ;" or, " In what relation a notion stands to the 
one of two \to if] subordinate notions, in the same relation stands 
it also to the other." 

§ 100. Fourth Figure ; fundamental rule : — " As a notion is 
determined by the oneoftiuo subordinate notions^ [tivo notions in 
the relation to each other of subordination^ so does it determine 
the other;" or, "In what relation one of two subordinated notions, 
[notions reciprocaUy std)ordinate or superordinate], stands as to 
a third, in the same relation stands it also to the other." 

[b) Fundamental Laws of Syllogism. — Eefeeences. 
(See Galluppi, Lezioni di Logica e di Metafisica, Lez. xlvii., 
vol. i. p. 345 d seq. ; Troxler, logik, i. p. 33 ; Bolzano, Wissens- 
chaftslehre, logik, vol. ii. § 263, p. 543.) 

I. Logicians who confound the Nota notfe and the Dictum de 
Omni, being ignorant of their several significances ; making them — 

a) Co-ordinate laws without distinction. 

Jager, Handb. d. Logik, § 68, (1839) ; Prochazka, Gesetjzb., 
fd.,Denken,% 217, (1842) ;'Calker, Denklehre, § 143, (1822). 
Troxler, Logik, ii. p. 40. 

b) Derivative ; the Dictum de Omni, to wit, from the Nota 
notte. This supreme or categorical. 

Wenzel, Elem. Philos. Log.., §§ 253, 256. Canonik, § 64. 
Kant, Diefalsche Spitzf, § 3. Logik, § 63. Krug, Logik, § 70. 
Bachmann, Logik, § 123. Jakob, Logik, § 262, 4th ed. 1800 ; 1st 
ed. 1788. 

II. Logicians who enounce the law of Identity, (Proportion,) in 
the same third, by the mathematical expression Equality. 

Reimarus, Vernunftlehre, § 176. Mayer, Vernunftschlusse, 
i. p. 290. Arriaga, In. Sum., D. III. § 3, p. 23. 

III. Logicians who make the Dictum de Omni the fundamental 
rule of syllogisms in general. 



310 APPENDIX. 

Aristot., An. Prior., L. i. c. 1, § 4 Wolf, PJiil. Rat, § 853. 
Schcibler, Op. P. iv. De Si/ll c. ii. § 12. Jac. Thomasius, Erot 
Log., c. 395. Buttner, Cursus Philos., Log., § 146. Conimbri- 
censes, Ln Arist. Dial., An. Prior., L. i. c. 2, p. 204. 

IV. Logicians wlio confound or make co-ordinate the law of 
Proportion or Analogy, and the Dictum de Omni. 

Wyttenbach, Prcec. Philos. Log., P. iii. c. 6, § 4. Whately, Logic, 
Intr., ch. II. p. iii., § 2. Leechman, Logic, P. III. eh. 2. Kecker- 
mann, Sy sterna Logicoe Minus, L. iii. c. 2. Syst. Log. Majus., 
L. iii. c. 5. 

V. Logicians who make the Law of Identity the one supreme. 

Suter, Logica, § 61, calls this the principle of Identity and Con- 
tradiction. Aldrich, Comp. L. i. c. 3, § 2, p. 2. Hutcheson, Log. 
Comp.,V. iii. c. 2. Arriaga, Gur. Phil., Ln. Sum., D. iii. §§ 16-22, 
pp. 23, 24. Larroque, Logique, p. 224. Mayer, Vernunftschlusse,\. 
p. 293. Troxler, Logik, ii. pp. 33, 40. Eeimarus, Vernunftlehre, 
§ 176. Mendoza, Disp. Log. et Met., I. p. 470. Derodon, Log. 
Rest., De Log. pp. 639, 644. Darjes, Via., &c., § 271, p. 07. Smigle- 
cius, Logica, D. xiii. p. 517. qu, &c. Fran. Bonae Spei, Com. 
Prim, in Log. Arist., D. vii. d. 2, p. 25. Cursus Complut, De 
Arg., L. iii. c. 4, p. 57. Alstedius, Lnc, Logica, § ii. c. ]0, p. 435. 
Havichorst, Lnst. Log., § 323. Poncius, Cursus Philos. Ln An. 
Pi'ior., D. XX. qu. 5, p. 282. 

VI. Logicians who restrict the Dictum de Omni to the first 
Figure (immediately). 

Aldrich, Comp. 1. 1, c. 3, § 7. Noldius, Log. Rec, c. xii. p. 
290. Grosser, Pharus LnteUectus, § iii. p. 1, memb. iii. p. 137. 

VII. Logicians who make the Dicta de Omni et NuUo the 
supreme canons for Universal Syllogisms ; the law of Proportion for 
Singular Syllogisms. 

Burgersdicius, Lnst. Log., L. ii. c. 8, p. 171. Melancthon, 
Erot. Dial, De Syll. Expos., L. iii. p. 172, ed. 1586. Fonseca, 
Lnstit. Dial, L. vi. cc. 21, 24, pp. 363, 373. 

VIII. • What name given by what logicians to the Law of Pro- 
i:)ortion, &c. 

Law of Proportion, or of Analogy, Keckermann, Syst. Log., 
L. iii. c. 5, Op., p. 746. Alstedius, Encycl.., p. 435, to ava\oyia<;. 
Dictum de Omni et Nulla Majus, Noldius, Log., p. 288. Of 
Ldentity, Zedler's Lex. Pr. convenientim, Darjes, Via ad Verit, § 
270, p. 96. Law of proportional Identity and Non-Identity, Self. 



APPENDIX. Oil 

IX. Logicians erroneously supposing Aristotle to employ, besides 
the Dictum de Omni, the rule of Proportion as a fundamental law 
of syllogism. 

Kapin, Reflexions sur la Logique, § 4. 

X. Terms under which the law of Proportion has been enounced. 
Agree ivith. Coincide tuith. The same with. (7o7iere, (Syrbius). 

Co-exist (bad). Co-identical with. Equal to, (No. ii.) In com- 
bination ivith, Darjes, Via ad Ver. p. 97, (includes negative.) 
Convertible. 

(c) Enunciations of the Higher Laws of Syllogism. 

Law of Proportion. 

Aristotle, ElencJi, c. vi. § 8. " Things the same with one and 
the same, are the same with one another." Compare Topica, L. vii., 
c. 1, § 6. Thus Scotus, In An. Prior., L. i. qu. 9, £ 2^8. 

Some say, "Uni tertio indivisibili" — some others, "Unitertio 
indivisibili, iudivisibiliter sumpto." Others, in fine, say, " Uni 
tertio, adequate sumpto." See Irenseus, Integ. Philos. Log., §§ 3, 
5. Some express it, " Things that are equal to the same third are 
equal to each other." See Irena^us, ib. So Reimarus, Mayer. 

Some express it, " Qutecunque conveniunt, (vel dissentiunt), in 
uno tertio, eadem conveniunt, (vel dissentiunt), inter se." 

" Quce duo conveniunt cum uno quodam tertio, eatenus conveni- 
unt inter se ; quando autem duorum unum convenit cum tertio, 
et alterum huic repugnat, repugnant quoque eatenus sibi invicem," 
Wynpersse, Inst. LogiccB, § 272, Lug. Bat. 3d ed. 1806. 

Noldius, {Logica, p. 288), calls these the Dicta de Omni et de 
Nullo. The former is, " Qusecunque affirmantur in aliquo tertio, 
(singulari identice, universal! et identice et complete distributive), 
afl&rmantur inter se." The latter, " Quorum unum [totaliter] affir- 
matur in aliquo tertio, alterum negatur, ea inter se negantur." 

Noldius.— " Whatever is affirmed essentially of a subject, is 
affirmed of all that is inferior or reciprocal to that subject. What- 
ever is denied of a subject, is denied of all inferior or reciprocal."' 
(See Noldius against the universal application of these Dicta, Log. 
Rec. p. 290). 

Reusch, {Syst Logicum, ed. i. 1734, § .503) makes the Dicta 
de Omni et Nullo the rule of ordinary syllogisms, and thus enunci- 
ates them, " Si quid prc^edicatur de omni, illud etiam prredicatur de 
aliquo : et, Si quid predicatur de nullo, illud etiam non prsedicatur 



342 APPENDIX. 

de aliquo. Sensus prions est, Quidquid de genere, vol specie 
omni prffidicari potest, illud etiam prsedicatur de quovis sub illo 
genere, vel sub ilia specie, coiitento ; Item, — Cuicunque corn- 
petit definitio, illi qiioque competit defiiiitum : " (and so vice versa 
of the other). 

Syrbius gives these two rules : — 

1) "If certain ideas cohere with a one-third, they also cohere in 
the same manner with each other ; " 

2) " Ideas which do not cohere with the same one-third, these do 
not cohere with each other." (Given in the original by Waldin, 
Systema, p. 162. See also Acta Eruditorum, 1718, p. 833.) 
Syrbius things that the law of Proportion, unless limited, is false. 

Darjes, Via ad Veritatem, (1755), § 270, p. 96, 2d ed. 1764, 
" Two [things or notions] in combination with the same third, 
may be combined together in the same respect, (ea ration e), where- 
in they stood in combination with that third." (See further ; shows 
that other rules are derived from this.) 

Dictum de Omni, &c. 

Aristotle, Anal. Pr., L. i., c. i., § 11. 

" To be predicated, de Omni, universally is, when we can find 
nothing under the subject of which the other [that is, the predicate] 
may not be said ; and to be predicated de Nullo, in like manner." 

Jac. Thomasius, Erotemata Logica, 1670. 

" 40. What do you call the foundation of syllogism ? — The Dic- 
tum de Omni et Nullo. 

" 41, What is the Dictum de Omni ? — When nothing can be sub- 
sumed under the subject of the major proposition of which its j)re- 
dicate may not be affirmed. 

" 42. What is the Dictum de Nullo ? — When nothing can be sub- 
sumed under the subject of the major proposition of which its predi- 
cate is not denied." 

Thomasius notices that the first rule applies only to the affirma- 
tive moods of the first figure, Barbara and Darii ; the second only 
to the negative moods of the same figure, Celarent and Ferio. 

(cZ) Objections to the Dictum de Omni et Nullo. 

I. As a principle of syllogism in general. 

II. As a principle of the First Figure, as enounced by Aristotle. 
1°, Only applies to syllogisms in extension. 



APPENDIX. 343 

2°, Does not apjDly to individual syllogisms ; as, Peter is run- 
ning ; hut some man is Peter ; therefore, some man is running. 

(Arriaga, In. Summ., p. 24.) 

8°, Does not apply in co-extensive reasonings ; as, All trilateral 
is {all) triangular ; hut all triangular has three angles equal to 
two right angles ; ergo, &c. Arriaga, ih. 



Dictum de Omni et NuUo does not apply, 

1°, To the other Figures than the First. 

2°, Not to all the moods of First Figure, for in many of these the 
higher class is subjected to the lower. 

3°, The form of the First Figure does not depend upon the 
principle of the Dictum de Omni et Nullo. This imperfect ; not upon 
the thoroughgoing principle, that in this figure one notion is com- 
pared to a second, and this second with a third. 



(1 
(3 

(4 
(5 
(6 
(1 
(3 
(5 
(6 
(1 
(2 
(3 

(4; 

(6 

(7: 
(8: 



(e) General Laws of Syllogism in verse. 
Partibus ex puris sequitur nil (2) sive negatis. 
Si qua praeit partis, sequitur conclusio partis. 
Si qua negata prteit, conclusio sitque negata. 
Lex generalis erit, medium concludere nescit.« 
Univocusque ; (7) triplex ; (8) ac idem terminus esto.3 
Distribuas medium ; (2) nee quartus terminus adsit. 
Utraque nee pra^missa negans ; (4) nee particularis. 
Sectetur partem conclusio deteriorem ; 
Et non distribuat nisi cum praemissa, (7) negetve.r 
Terminus esto triplex : medius, majorque, minorque: 
Latins hunc quam pra3miss8e, conclusio non vult, 
Nequaquam medium capiat conclusio oportet. 
Aut semel aut iterum medium generaliter esto. 
Nil sequitur gemiuis ex particularibus unquam. 
Utraque si pra3missa neget, nihil inde sequetur. 
Amba3 affirmantes nequeunt generare negantem. 
Est parti similis conclusio deteriori. ") 

Pejorem sequitur semper conclusio partem, j ^ 



a, Petrus Hispanus, Summulce. [Tr. ^ Purchot, with variations of Seguy, 

iv. c. 3, f. 45 b.— Ed.] Ph. Lugd., Galluppi. [Purchot, Inst. 

jS Campanella, Dialect., p. 384. Phil., vol. i., Loyica, P. iii. c. 3, p. 17L 

7 Hutcheson, Log. Comp. [P. iii. c. — Ed.] 
3, p. S3.— Ed.] 



S44? APPENDIX. 

(1) Terminus est geminus, mecliumque accedit utriqiie. 

(2) Proemissis dicat ne finis plura, caveto. 

(3) Aut semel, aut iterum medium genus omne capessat ; 

(4) Officiique tenax rationem claudere nolit. 

(1) Terminus est triplex. (2) Medium conclusio vitet. 

(3) Hoc ex prtemissis altera distribuat. 

(4) Si praemissa simul fuit utraque particularis, 
{ (5) Aut utrinque negans, nulla sequela venit. 

(6) Particulare prseit ? sequitur conclusio partis. 

(7) Ponitur ante negans ? Clausula talis erit. 

(8) Quod non prascessit, conclusio nulla requirit.« 
Turn re, tum sensu, triplex modo terminus esto. 

{Argumentari non est ex particulari. 
Neque negativis recte concludere si vis. 
{Nunquam complecti medium conclusio debet. 
Quantum proemisssB, referat conclusio solum, 
f Ex falsis falsum verumque aliquando sequetur ; 
I Ex veris possunt nil nisi vera sequi.^ 

(/) Special Laws of Syllogism in veese. 

1. Fig. Sit minor affirmans, nee major particularis. 

2. Fig. Una negans esto, major vero generalis. 

3. Fig. Sit minor affirmans, conclusio particularis. 

4- Fig. a) Major ubi affirmat, generalem sume ininorem. 

b) Si minor affirmat, conclusio sit specialis. 

c) Quando negans modus est, major generalis hab- 

etur."/ 

B. Ceiticism. 
(a) Criticism op the Special Laws of Syllogism. 

The Special Laws of Syllogism, that is, the rules which govern 
the several Figures of Categorical Reasonings, all emerge on the 
suspension of the logical postulate, — To be able to state in language 
what is operative in thought. They all emerge on the refusal or 

a Isendoorn, Logica, L. iii. c. 8, p. 427, jx 210. 
8°, (1652). Chauviu and Walcb, Xc.r. i>. y Ubaghs, Logicce Elementa, § 225, 

Sijlloij. Saucrucius, Dialectica ad Mentem Doct- 

fi Crakauthorpe, Logica, L. iii. c. 15, HubtUis, L. i. c 3, p. 103. Lond. 1673. 



APPENDIX. 345 

neglect to give to the predicate that quantity in overt expression, 
which it possesses in the internal operations of mind. The logi- 
cians assert, 1", That in affirmative propositions the predicate 
must be always presumed particular or indefinite, though in this 
or that proposition it be known and thought as universal or defi- 
nite ; and, 2°, That in negative propositions this same predicate 
must be always presumed absolutely, {i. e. universally or definitely), 
excluded from the sphere of the subject, even though in this or that 
proposition it be known and thought as partially, {i. e. particularly 
or indefinitely), included therein. The moment, however, that the 
said postulate of Logic is obeyed, and we are allowed to quan- 
tify the predicate in language, as the predicate is quantified in 
thought, the special rules of syllogism disappear, the figures are 
all equalised and reduced to unessential modifications ; and while 
their moods are multiplied, the doctrine of syllogism itself is 
carried up to the simplicity of one short canon. Having already 
shown that the general laws of syllogism are all comprised and 
expressed in this single canon,« it now only remains to point 
out how, on the exclusive doctrine of the logicians, the special 
rules became necessary, and how, on the unexclusive doctrine 
which is now propounded, they become at once superfluous and 
even erroneous. It is perhaps needless to observe, that the follow- 
ing rules have reference only to the whole of Extension. 

The double rule of the First Figure, that is, the figure in which 
the middle term is subject in the sumption, and predicate in the 
subsumption, is, — Sit minor affirmans ; nee major particularis. 
Here, in the first place, it is prescribed that the minor premise 
must be affirmative. The reason is manifest. Because if the minor 
premise were negative, the major premise behoved to be affirma- 
tive. But in this figure, the predicate of the conclusion is the 
predicate of the major premise; but, if affirmative, the predicate of 
that premise, on the doctrine of the logicians, is presumed par- 
ticular, and as the conclusion following the minor premise is 
necessarily negative, a negative proposition thus, contrary to logi- 
cal law, has a particular predicate. But if we allow a negative 
proposition to have in language, as it may have in thought, a 
particular or indefinite predicate, the rule is superseded. 

a See above, p. 285, and below, p. 350. — Ed. 



34G APPENDIX. 

The second mle, or second part of the rule, of this First Figure, 
is, that the major premise should be nniversal. The reason of 
this is equally apparent. For ■we have seen, that, by the previous 
rule, the minor premise could not be negative, in which case 
certainly, had it been allowable, the middle term would, as predi- 
cate, have been distributed. But whilst it behoved that the middle 
term should be once at least distributed, ^or taken universally), 
and, as being the subject of the major premise, it could only be 
distributed in a universal proposition, the rule, on the hypothesis 
of the logicians, was compulsory. But as we have seen that the 
former rule is, on our broader ground, inept, and that the middle 
term may be universally quantified, as the predicate either of an 
affirmative or negative subsumption, it is equally manifest that this 
rule is, in Hke manner, redimdant, and even false. 

In the Second Figure, that is, the figure in which the middle 
term is predicate both in sumption and subsimiption, the special 
mle is, — Una negans esto; major vero generalis. 

In regard to the first rule, or first half of the rule, — That one 
or other of the premises should be negative. — the reason is mani- 
fest. For, on the doctrine of the logicians, the predicate of an 
affirmative proposition is always presumed to be particular ; con- 
sequently, in this figure the middle term can, on their doctrine, 
only be distributed, (as distributed at least once it must be , in a 
negative judgment But, on our doctrine, on which the predicate 
is quantified in language as in thought, this rule is abolished, a 

The second rule, or second moiety of the rule, — That the sump- 
tion should be always universal, — the reason of this is equally 
clear. For the logicians, not considering that both extremes were 
in equilibrio in the same whole of extension, and, consequently, 
that neither could claim in. either quantity] the place of major or 
minor term, and thereby constitute a true major or a true minor 

a [For examples from Aristotle of affirm- positions in Second Figure, and does 
ative conclusions in the Second Figure, not give the reason why the inference is 
see De C(bIo. L. iL, c. 4, § 4, text 23, ibi good or bad in such syllogism. Cf. Am- 
Averroes. PTiyi. L. iL, c. 2, § 12, text monius and Philoponus ad. loc An, 
23, ihi Averroes ; c. 4, § 8, text 33, ibi Prior, L. ii, c. 22, §§ 7, 8. An. Post., 
ATerroes. Ih.c. 7,§ 1, text 42, S* Aver- L. i, c 6, § 1, cf ibi, Themistius, Pa- 
roes. ^n.Po*f,L. i.c. 12,§ 12,text92, cius, ZabareUa. Cf. also Zabarella, De 
ibi Arerroes et Pacius. Argues himself, Quarta Fig. SyTl., c x.] 
like Caeneus, from two aSSrmatlYe pro- 



APPENDIX. 347 

premise ; — the logicians, I say, arbitrarily drew one instead of 
two direct conclusions, and gave tlie name of major term to tliat 
extreme which formed the predicate in that one concltision, and 
the name of major premise to that antecedent proposition which 
they chose to enounce first. On their doctrine, therefore, the 
conclusion and one of the premises being always negative, it 
behoved the sumption to be always general, otherwise, contrary to 
their doctrine, a negative proposition might have a particular pre- 
dicate. On our doctrine, however, this difficulty does not exist, 
and the rule is, consequently, superseded. 

In the Third Figure, that is, the figure in which the middle 
t^rm is subject of both the extremes, the special rule is, — Sit 
minor afirmans; conclusio paHicularis. 

Here the first half of the rule, — That the minor must not be 
negative, — is manifestly determined by the common doctrine. 
For, major and minor terms, major and minor propositions, being 
in this figure equally arbitrary as in the second , here the stmiprion 
behoving to be afiirmative, its predicate, constituting the major 
term or predicate of the conclusion, behoved to be particular also. 
But the conclusion following the minor premise wotild necessarily 
be negative ; and it would have, — ^what a negative proposition is not 
allowed on the common doctrine, — an tmdistribute^i predicate. 

The second half of the rtde, — That the concltision mtist be 
partictilar, — is determined by the doctrine of the logicians, that 
the particular antecedent, which they choose to caU the minor 
term, should be affirmative. For, in this case, the middle term 
being the subject of both premises, the predicate of the subsump- 
tion is the minor extreme ; and that, on their doctrine, not being 
distributed in an affirmative proposition, it consequently, forms 
the undistributed subject of the conclusion. The conclusion, 
therefore, having a particular subject, is, on the common doctrine, 
a particular proposition. But as. on our doctrine, the predicate 
of an affirmative proposition may have an universal quantification, 
the reason fails. 

(6) Laws of Second Figuee — ADDrnoxAL." 
By designating the quantity of the predicate, we can have the 

a Wliat follows to page 349 «as an in Ltftnrts (yoL L p. 408), being an ap- 

earlj- written interpolation by the auziior plication of the principle of a quantiSed 



348 APPENDIX. 

middle term, (wliich in this figure is always a predicate), distributed 
in an affirmative proposition. Thus : — 

AWPisallM; 
All Q is S07ne M ; 
Therefore, all S is some P. 

All the things that are organised are all the things that are endowed 

with life ; 
But all 2Jlants are some things endoived with life; 
Therefore, all plants are some things organised. 

This first rule (see above, Vol. I. p. 408) must, therefore, be thus 
amplified : — The middle term must be of definite quantity, in 
one premise at least, that is, it must either, 1°, Be a singular, — 
individual, — concept, and, therefore, identical in both premises ; or, 
2°, A universal notion presumptively distributed by negation in 
a single premise ; or, 3°, A universal notion expressly distributed 
by designation in one or both premises. 

But the second rule, which has come down from Aristotle, and 
is adopted into every system of Logic, with only one exception, an 
ancient scholiast, is altogether erroneous. For, 1°, There is pro- 
perly no sumption and subsumption in this figure ; for the 
premises contain quantities which do not stand to each other in 
any reciprocal relation of greater or less. Each premise may, 
therefore, stand first. The rule ought to be, " One premise must be 
definite ; " but such a rule would be idle ; for what is here given 
as a special canon of this figure, was aheady given as one of the 
laws of syllogism in general. 2°, The error in the principle is 
supported by an error in the illustration. In both the syllogisms 
given," the conclusion drawm is not that which the premises war- 
rant. Take the first or affirmative example. The conclusion here 
ought to have been. No S is some P, or Some P is no S ; for 
there are always two equivalent conclusions in this figure. In 
the concrete example, tlie legitimate conclusions, as necessitated 
by the premises, are, — No horse is some animal, and, Soryie 
animal is no horse. This is shoAvn by my mode of explicating 

predicate tu syllogism. The interpola- probably given still earlier. — Ed, 
tion appears in students' notes of the a See above, vol. i. p. 409. — Ed. 
Lectures of session 1841-42 ; and was 



APPENDIX. 349 

the quantity of the predicate, — combined with my symbolical 
notation. In like manner, in the second or negative syllogism, the 
conclusion ought to have been either of the two following : In the 
abstract formula, — All S are not some P ; or. Some P are not all 
S ; — in the concrete example, All topazes are not some minerals, 
i. e., No topazes are some minerals; or, Some minerals are not 
all topazes, i. e., Some miney^als are no topazes. 

The moods Cesare and Camestres may be viewed as really one, 
for they are only the same syllogism, with premises placed first or 
second, as is always allowable in this [Figure], and one of the two 
conclusions, which are always legitimately consequential, assigned 
to each. 

A syllogism in the mood Festino, admits of either premise being 
placed first ; it ought, therefore, to have had another mood for its 
pendant, with the affirmative premise first, the negative premise 
second, if we are to distinguish moods in this figure by the acci- 
dental arrangement of the premises. But this was prohibited by 
the second Law of this Figure, — that the Sumption must always 
be universal. Let us try this rule in the foimula of Festino now 
stated, reversing the premises. 

Some S are M ; (i. e., some M.) 
No P is M ; 

( No P is some S. 



{ J\o ir IS some a. ) 
I Some S are no P. j 



Some actions are praiseworthy ; 
No vice is 2:)7'aiservorthy ; 

( No vice is some action. ) 
\ Some action is no vice. ) 

From what I have now said, it will be seen that the Dictum de 
Omni et de Nullo cannot afford the principle of the Second Figure. 
The same errors of the logicians, on which I have already com- 
mented, in supposing that the sumption or major premise in this 
figure must always be universal, — an error founded on another 
error, that there is, (properly speaking), either sumption or sub- 
sumption in this figure at all, — this error, I say, has prevented them 
recognising a mood corresponding to Baroco, the first premise 
being a particular negative, the second a universal affirmative, i. e., 
Baroco with its premises reversed. That this is competent is 



SoO APPENDIX. 

seen from the example of Baroco now given. Eeversing it we 
have : 

[Some d are not B ; Some aniinals are not {any) oviparous; 

Alt di are B. All birds are {some) ovijyarous. 

No a is somQ d; No bird is some animal; 

Some d are no a.] Some animal is no bird. 

(c) Author's Supreme Canons of Categorical Syllogisms. 

[The supreme Canon or Canons of the Categorical Syllogism, 
finally adopted by Sir W. Hamilton, are as follow :— ] 

I. " For the Unfigured Syllogism, or that in which the terms 
compared do not stand to each other in the reciprocal relation of 
subject and predicate, being, in the same proposition, either both 
subjects or (possibly) both predicates, — the canon is: — I)i so far 
as two notions, (notions proper, or individuals), either both agree, or 
one agreeing, the other does not, ivith a common third notion ; in 
so far, these notions do or do not agree with each others 

II. " For the Figured Syllogism, in which the terms compared 
are severally subject and predicate, consequently, in reference to 
each other, containing and contained in the counter wholes of In- 
tension and Extension ; — the canon is : — What worse relation of 
subject and predicate subsists between either of two terms and a 
common thirds term, with ivhich one, at least, is positively re- 
lated; that relation subsists between the tiuo terms themselves. 

" Each Figure has its own Canon. 

"First Figure ; — What worse relation of detei-mining, {predi- 
cate), and of determined, (subject), is held by either of two 
notions to a third, with which one at least is jjositively related ; 
that relation do they immediately, (directly), hold to each other, 
and indirectly, (mediately), its converse 

"Second Figure ; — Wliat ivorse relation of determined, (sub- 
ject), is held by either of two notions to a, third, tuith which one 
at least is positively related ; that relation do they hold indif- 
ferently to each other 

" Third Figure; — What luorse relation of determining (predi- 
cate), is held by either of two notions to a third, with which one 
at least is positively related ; that relation do they hold indiffer- 
ently to each other." "■ 

«■ Discussioiis, pp. 654, 055. — Ed. 



APPENDIX. 351 

{d) Ultra-total Quantification of Middle Term. 
(1.) Lambert's Doctrine. 

Lambert, Neues Organon. 

Dianoiologie, § 193. "If it be indetermined how far A does, 
or does not, coincide with B, but on the other hand we know that 
A and B, severally, make up more than half, * the individuals 
under C, in that case it is manifest, that a [linear] notation is 
possible, and that of the two following kinds : — 

C c, 

B b, 

A 

" For since B and A are each greater than the half oi C, A is 
consequently greater than C less by B ; and in this case, it is of 
necessity that some A are B, and some B are A.^ We may 
accordingly so delineate : — 

C c, 

A a, 



B b, 

seeing that it is indifferent, whether we commence with A or with 
B. I may add, that the case which we have here considered does 
not frequently occur, inasmuch as the comparative extension of 
our several notions is a relation which remains wholly unknown.y 
I, consequently, adduce this only as an example, that a legitimate 
employment may certainly be made of these relations." 

« It is enough if either A or B ex- counter to each other, with which Logic 

ceed the halt' ; the other need be only is alwaj's conversant, (the Universal and 

half. This, which Lambert here and Formal), — if the extension be not com- 

hereafter overlooks, I have elsewhere plate, it is of no consequence to note its 

had occasion to show. See below, p. 356. comparative amount. For Logic and 

/3 In the original for A there is, by a Philosophy tend always to an unexclu- 

typographical erratum, C. See PA. §208. sive generality; and a general conclu- 

7 In reference to this statement, see sion is invalidated equally by a single 

above, Z> /cm. § 179, and below, PA. § 157, adverse instance as by a thousand. It 

where it is repeated and confirmed. Lain- is only in the concrete or real whole, — 

bert might have added, that, as we rarely the whole quantitative or integrate, and, 

can employ this relation of the compai-a- whether continuous or discrete, the 

tive extension of our notions, it is still whole in which mathematics are exclu- 

morerarely of any import that we should, sively conversant, but Logic and Philo- 

For in the two abstract, or notional, sopby little interested, — that this rela- 

wholes, — the two wholes correlative and tiou is of any avail or significance. 



352 APPENDIX. 

Phdnomenolugie, § v. Of the Prohahle — 

" § 188. In so far as such propositions are particular, they may, 
like all other particular propositions, be syllogistically employed ; 
but no farther, unless we look to their degree of particularity, or 
other proximate determination, some examples of which we have 
adduced in the Dianoiologie, (§ 235 et seq.) Thus the degree of 
ixarticularity may render a syllogism valid, which, without this, 
would be incompetent. For example — 

Three-fourths of A are B ; 
Two-thirds of A are G ; 
Therefore, some C are B. 

The inference here follows, because three-fourths added to two- 
thirds are greater than unity ; and, consequently, there must be, 
at least, five-twelfths of A, wliich are at once B and C. 

" § 204. In the Third Figure we have the middle term, subject 
in both premises, and the conclusion, particular. If now, the 
subjects of the two premises be furnished with fractions [i.e. the 
middle term on both sides], both premises remain, indeed, parti- 
cular, and the conclusion, consequently, indetermined. But, inas- 
much as, in both premises, the degree of particularity is determined, 
there are cases where the conclusion may be drawn not only with 
probability, but with certainty. Such a case we have already 
adduced, (§ 188). For, if both premises be affirmative, and the 
sum of the fractions with which their subjects are furnished greater 
than unity, in that case a ccmclusion may be drawn. In this sort 
we infer with certainty : — 

Threefourths of A are B ; 
Two-thirds of A ai'e ; 
Therefore, some C are B. 

" § 205. If, however, the sum of the two fractions be less than 
unity, as — 

Onefourth of A are B ; 
One-third of A are C, 

in that case there is no certainty in any affirmative conclusion, 
[indeed in any conclusion at all]. But if we state the premises 
thus determinatelv, — 



APPENDIX. 353 

Three-fourths of A. are not B ; 
Two-thirds of A. are not C ; 

in that case, a negative conclusion may be drawn. For, from the 
propositions, — 

Threefourths of A are not B; 
One-third of A are C ; 

there follows — Some C are not B. And this, again, because the 
sum of the two fractions, (three-fourths added to one-third), is 
greater than unity." And so on ; see the remainder of this section 
and those following, till § 211. 



(2). Author's Doctrine. 

Aristotle, followed by the logicians, did not introduce into his 
doctrine of syllogism any quantification between the absolutely 
universal and the merely particular predesignations, for valid rea- 
sons. — 1°, Such quantifications were of no value or application in 
the one whole, (the universal, potential, logical), or, as I would 
amplify it, in the two correlative and counter wholes, (the logical, 
and the formal, actual, metaphysical), with which Logic is con- 
versant. For all that is out of classification, — all that has no refer- 
ence to genus and .species, is out of Logic, indeed out of Philosophy ; 
for Philosophy tends always to the universal and necessary. Thus 
the hio;hest canons of deductive reasoning, the Dicta de Omni et 
de Xullo, were founded on, and for, the procedure from the uni- 
versal whole to the subject parts ; whilst, conversely, the principle 
of inductive reasoning was established on, and for, the (real or pre- 
sumed) collection of all the subject parts as constituting the uni- 
versal whole. — 2°, The integrate or mathematical whole, on the 
contrary, (whether continuous or discrete), tlie philosophers con- 
temned. For whilst, as Aristotle observes, in mathematics genus 
and species are of no account, it is, almost exclusively, in the 
mathematical whole, that quantities are compared together, through 
a middle term, in neither premise, equal to the whole. But this 
reasoning, in which the middle term is never universal, and the 

VOL. II. Z 



354 APPENDIX. 

conclusion always particular, is, — as vague, partial, and contingent, 
— of little or no value in philosophy. It was accordingly ignored 
in Logic ; and the predesignations mo7-e, most, &c., as I have said, 
referred to universal, or (as was most common) to particular, or to 
neither, quantity.'' This discrepancy among logicians long ago 
attracted my attention ; and I saw, at once, that the possibility of 
inference, considered absolutely, depended, exclusively on the quan- 
tifications of the middle term, in both premises, being, together, 
more than its possible totality — its distribution, in any one. At 
the same time I was impressed — 1°, With the almost utter inutility 
of such reasoning, in a philosophical relation ; and, 2°, Alarmed with 
the load of valid moods which its recognition in Logic would in- 
troduce. The mere quantification of the predicate, under the two 
pure quantities of definite and indefinite, and the two qualities of 
afiirmative and negative, gives (abstractly) in each figure, thirty- 
six valid moods ; which, (if my present calculation be correct), 
would be multiplied, by the introduction of the two hybrid or am- 
biguous quantifications of a majority and a half, to the fearful 
amount oi four hundred and eighty valid moods for each figure. 
Though not, at the time, fully aware of the strength of these ob- 
jections, they however prevented me from breaking down the old 
limitation ; but as my supreme canon of Syllogism proceeds on the 
mere formal possibility of reasoning, it of course comprehends all 
the legitimate forms of quantification. It is ; — Wliat ivorst 
relation of subject and j^^'edicate, subsists hetiveen either of two 
terms and a common thii^d term, with which one, at least, is 
positively related ; — that relation subsists between the two terms 
themselves : in other words ; — In as far as two notions both agree, 
or, one agreeing, the other disagrees, with a common third notion; 
— in so far, those notions agree or disagree ivith each other. This 
canon applies, and proximately, to all categorical syllogisms, — in 
extension and comprehension, — affirmative and negative, — and of 
any figure. It determines all the varieties of such syllogisms : is 
developed into all their general, and supersedes all their special, 
laws. In short, without violating this canon, no categorical rea- 
soning can, formally, be wrong. Now this canon supposes, that 

o [Cf. Corvinus, Instit. Phil. c. v. § Wallis, Instit. Log. L. ii. c. i, p. 100. 
376, r- 123. lence, 1742. Reusch, 5th ed.— Ed.] 
Wallis.] [Reusch, Syst. Log. § 360. 



APPENDIX. 355 

the two extremes are compared together through the saiiie com- 
mon middle ; aud this cannot but be, if the middle, whether, sub- 
ject or predicate, in both its quantifications together, exceed its 
totality, though not taken in that totality in either premise. 

But, as I have stated, I was moved to the reconsideriition of this 
whole matter ; and it may have been Mr De Morgan's syllogism 
in our correspondence, (p. 19), which gave the suggestion. The 
result was the opinion, that these two quantifications should be 
taken into account by Logic, as authentic forms, but then relegated, 
as of little use in practice, and cumbering the science with a super- 
fluous mass of moods." 



Authoe's Doctrine — continued. 

No syllogism can be formally wrong in which, (1°), Both jire- 
mises are not negative ; and, (2°), The quantifications of the middle 
term, whether as subject or predicate, taken together, exceed the 
quantity of that term taken in its whole extent. In the former 
case, the extremes are not compared together ; in the latter, they 
are not necessarily compared through the same third. These two 
simple rules, (and they both flow from the one supreme law), being 
obeyed, no syllogism can be bad ; let its extremes stand in any 
relation to each other as major and minor, or in any relation to 
the middle tei^m. In other words, its premises may hold any 
mutual subordination, and may be of any Figure. 

On my doctrine, Figure being only an unessential circumstance, 
and every proposition being only an equation of its terms, we 
may discount Figm-e, &c., altogether ; and instead of the symbol 
{ mm ) marking subject and predicate, we might use the alge- 
braical sign of equality (=). 

The rule of the logicians, that the middle term should be once at 
least distributed, [or indistributable], {i. e., taken universally or sin- 
gularly = definitely), is untrue. For it is sufficient if, in both the 
premises together, its quantification be more than its quantity as a 
whole, (Ultratotal). Therefore, a major part, (a more or mosi), in 
one premise, and a half in the other, are sufficient to make it eSec- 
tive. It is enough for a valid syllogism, that the two extreme notions 

« Extract from A Letter to A. de p. 41. — Ed. 
Moj-i/an, Esq., from Sir W. Haniillm, 



356 APPENDIX. 

should, (or should not), of necessity, partially coincide in the third, 
or middle notion ; and this is necessarily shown to be the case, if 
the one extreme coincide with the middle, to the extent of a half, 
(Dimidiate Quantification) ; and the other, to the extent of aught 
more than a half, (Ultradimidiate Quantification). The first 
and highest quantification of the middle term ( : ) is sufiicient, 
not only in combination with itself, but with any of all the three 
inferior. The second ( . , ) suffices in combination with the high- 
est, with itself, and with the third, but not with the lowest. The 
third ( . ) suffices in combination with either of the higher, but not 
with itself, far less with the lowest. The fourth and lowest ( , ) 
suffices only in combination with the highest. [1. Definite; 2. 
Indefinito-definite ; 3. Semi-definite ; 4. Indefinite.] 



(ist March 1847. — Very carefully authenticated.) 
There are 4 quantities (, | . | ., | : ), affording (4 x 4), 16 pos- 
sible double quantifications of the middle term of a syllogism. 



Of these 10 are legitimate equivalents, (^: M : | : M. , | . , M , 



: M . I . M : I : M , I , M : 1 . , M. , I . , M . I . M . , ) ; and 6 
illegitimate, as not, together, necessarily exceeding the quantity 
of that term, taken once in its full extent ( . , INI , | , ^I • , | • M . | 
.M, |,M. |,M,). 

Each of these 16 quantified middle terms affords 64 possible 
moods ; to wit, 16 affirmative, 48 negative ; legitimate and ille- 
gitimate. 

Altogether, these 16 middle terms thus give 256 affirmative and 
768 negative moods ; which, added together, make up 1024 moods, 
legitimate and illegitimate, for each figure. For all three figures 
= 3072. 

The ] legitimate quantifications of the middle terra afford, of 
legitimate moods, 160 affirmative and 320 negative (=480) i.e. 
each 16 affirmative and 32 negative moods, (=48) ; besides of 
illegitimate moods, from double negation, 160, i.e., each 16. The 
6 illegitimate quantifications afford, of affirmative moods, 96 ; of 



APPENDIX. 357 

simple negative moods, 192 ; of double negative moods, 96 (= 
384). Adding all the illegitimates =544. 

The 1024 moods, in each figure, thus afford, of legitimate, 480 
moods, (1440 for all 3 Figs.) ; being of affirmative 160 (480 for 3 
Figs.), of negative 320 (960 for 3 Figs.), of illegitimate 544 moods ; 
there being excluded in each, from inadequate distribution alone, 
(§), 288 moods, (viz. 96 affirmative 192 negative) ; from double 
negation alone, (|), 160 moods ; from inadequate distribution and 
double negation together, (§ j), 96 moods. 



(.3). Mnemonic Verses. 

A it affirms of this, tliese, all — 
Whilst E deuies of any : 

I, it affirms, whilst denies, 
Of some (or few or many). 

Thus A affirms, as E denies, 

And definitely either : 
Thus I affirms, as denies, 

And definitely neither. 

A half, left semi-definite, 

Is worthy of its score ; 
U, then, affirms, as Y denies, 

This, neither less nor more. 

Indefinite -definites, 
To UI and YO we come ; 

And that affirms, and this denies, 
Of more, most, (half plus some.) 



UI and YO may be called Indefinito-definite, either, (T), Because 
they approximate to the whole or definite, [forming] more than its 
moiety, or, (2°), Because they include a half, which, in a certain 
sense, may be regarded as definite, and something, indefinite, over 
and above. 



358 APPENDIX. 

VII.— INDUCTION AND EXAMPLE. 

(See above, vol. i., p. 318.) 
(a) Quotations feom Authors. 

I. — Aristotle. 

Aristotle, Prior Analytics, B. ii. c. 23. After stating that "we 
believe all things either through [deductive] Syllogism or from In- 
duction," he goes on to expound the nature of this latter process. 

" Now, Induction, and the Syllogism from Induction, is the 
inferring one extreme, [the major], of the middle through the 
other ; if, for instance, B is the middle of A C, and, through C, 
we show that A inheres in B. Thus do we institute Inductions. 
In illustration : — Let A be long-lived, B, wanting-hile, and C, 
individual long-lived animals, as man, horse, mule, &c. A, then, 
inheres in the whole of C, (for all animal without hile is [at least 
some] long-lived) ; but B, wanting hile, also [partially, at least] 
inheres in all C.« If now C reciprocate with B, and do not go 
beyond that middle, [if C and B, subject and predicate, are each 

«- I have, however, doubts whether thus: — the individual animals wanting 

the example which now stands in the bile are [all] long-lived ; consequently, 

Organon, be that which Aristotle hira- [all] animals wanting bile are long-lived." 

self proposed. It appears, at least, to F. 107, a. ed. Aid. Compare also the 

have been considerably modified, pro- greatly later Leo Magentinus, on the 

bably to bring it nearer to what was Prior Analytics, f. 41, a. ed. Aid. On 

subsequently supposed to be the truth, the age of Magentinus, historians (as 

This I infer as likely from the Commen- Saxius and Fabricius,) vary, from the 

tary of Ammonius on the Prior Ana- seventh century to the fovirteenth. He 

lytics, occasionally interpolated by, and was certainly subsequent to Michael 

thus erroneously quoted under the Psellus, junior, whom he quotes, and, 

name of a posterior critic, — Joannes, therefore, not before the end of the 

surnamed Philoponus, &c. His woi-ds eleventh century ; whilst his ignorance 

are, in reference to Aristotle, as follows : of the doctrine of Conversion, introduced 

— " He wishes, through an example, to by Boethius, may show that he could 

illustrate the Inductive process ; it is of hardly have been so recent as the four- 

this intent. Let A be long-lived; B, teenth. 

wanting hile; G, as crow, and the like. Aristotle, De Part. Animal, (L. iv. c. 

Now he says: — that the crow and the stag, 2), says, "in some animals the gall 

being animals without bile and long- [bladder] is absolutely wanting, as in the 

lived ; therefore, animal wanting bile is horse, mule, ass, stag, and roe.". . . "It 

long-lived. Thus, tlu-ough the last [or is, therefore, evident that the gall serves 

minor], do we connect the middle term no useful purpose, but is a mere excre- 

with the [major] extreme. For I argue tion. Wherefore those of the ancients say 



APPENDIX. 



359 



all tlie other], it is of necessity that A, [some, at least], should 
inhere in [all] B, Por it has been previously shown,« that if any 
two [notions] inhere in the same [remote notion], and if the 
middle ^ reciprocate with either [or with both] ; then will the 
other of the predicates [the syllogism being in the third figure] 
inhere in the co-reciprocating extreme. But it behoves us to con- 
ceive C as a complement of the wliole individuals ; for Induction 
has its inference through [as it is of] all. 7 



■«'ell, who declare that the cause of lon- 
gevity is the abseuce of the gall ; and this 
from their observation of the solidun- 
gula and deer, for animals of these 
classes want the gall, and are long-lived." 
Hist. An., L. ii. c. 11, Schn. 18, Seal. 15 
vul. Notices that some animals have, 
others want, the gall bladder, {xo>^h, v. 
Schn. iii. p. 1 06), at the liver. Of the latter, 
among viviparous quadrupeds, he notices 
stag, roe, horse, mule, ass, &c. Of birds 
who have the gall-bladder apart from 
the liver and attached to the intestines, 
he notices the pigeon, crow, &c. 

* Aristotle refers to the chapter im- 
mediately preceding, which treats of the 
Reciprocation of Terms, and in that to 
the fifth rule which he gives, and of the 
following purport. " Again, when A and 
B inhere in all C [/.e. all C is A and is B], 
and when reciprocates [i.e. is of the 
same extension and comprehension] with 
B, it is necessary that A should inhere in 
all B [i.e. that all B should be A] ." 

)3 For oLKpov, I read /JLeaov ; but per- 
haps the true lection is — irphs tovto 
Barepov uvrSiiv avTi(rTpe<prj twv &Kpoov. 
The necessity of an emendation becomes 
manifest from the slightest consideration 
of the context. In fact, the common 
reading yields only nonsense ; and this 
on sundry grounds. — 1°, There are three 
things to which Odrepov is here appli- 
cable, and yet it can only apply to two. 
But if limited, as limited it must be, 
to the two inhei-ents, two absurdities 
emerge. 2°, For the middle, or common, 
notion, in which both the others inhere, 
that, in fact, here exclusively wanted, is 
alone excluded. 3°, One, too, of the in- 



herents is made to reciprocate with either ; 
that is, with itself, or other. 4°, Of the 
two inherents, the minor extreme is that 
which, on Aristotle's doctrine of Induc- 
tion, is alone considered as reciprocating 
with the middle or common term. But, 
in Aristotle's language, rh &Kpov, " The 
Extrem.e, " is (like t} irp6Ta<ris, The Pre- 
position in the common language of the 
logicians) a synonyme for the major, in 
opposition to, and in exclusion of, the 
minor, term. In the two short corre- 
lative chapters, the present and that 
which immediately follows, on Induc- 
tion and on Example, the expression, be- 
sides the instance in question, occurs at 
least seven times; and in all as the major 
term, — 5°, The emendation is required 
by the demonstration itself, to which 
Aristotle refers. It is foiind in the 
chapter immediately preceding (§ 5) ; 
and is as follows : — " Again, when A and 
B inhere in all C ; and when C recipro- 
cates with B ; it necessarily follows that 
A should [partially, at least], inhere in 
all B. For whilst A [some, at least], in- 
heres in all C ; and [all] C, by reason of 
their reciprocity, inheres in [all] B ; A 
will also [some, at least], inhere in all 
B." The mood here given is viii. of our 
Table. (See below. Appendix XI.) 

7 This requisite of Logical Induction, 
— that it should be thought as the re- 
sult of an agreement of all the indivi- 
duals or parts, — is further shown by 
Aristotle in the chapter immediately 
following, in which he treats the reason- 
ing from Example. See passage quoted 
on this page (§ 5). 



360 APPENDIX. 

" Tins kind of syllogism is of the primary and immediate pro- 
position. For the reasoning of things mediate is, through their 
medium, of things immediate, through Induction. And in a cer- 
tain sort, Induction is opposed to the [Deductive] Syllogism. For 
the latter, through the middle term, proves the [major] extreme 
of the third [or minor] ; whereas the former, through the third, [or 
minor term, proves] the [major] extreme of the middle. Thus, 
[absolutely], in nature, the syllogism, through a medium, is the 
prior and more notorious ; but [relatively] to us, that through In- 
duction is the clearer." 

An. Pr., L. ii. c. 24. Of Example. — § 1. "Example emerges, 
when it is shown that the [major] extreme inheres in the middle, 
by something similar to the third [or minor term] ... § 4. 
Thus it is manifest that the Example does not hold the relation 
.either of a whole to part [Deduction], nor of a part to whole 
[Induction], but of part to part ; when both are contained under 
the same, and one is more manifest than the other. § 5. And 
[Example] differs from Induction, in that this, from all the indi- 
viduals, shows that the [major] extreme inheres in the middle, and 
does not [like Deduction] hang the syllogism on the major ex- 
treme ; whereas that both hangs the syllogism [on the major ex- 
treme], and does not show from all the individuals [that the major 
extreme is inherent in the minor.]" 

An. Post., L. i. c. 1, § 8. — " The same holds true in the case of 
Teasonings, whether through [Deductive] Syllogisms or through 
Induction ; for both accomplish the instruction they afford from 
information foreknown, the former receiving it as it were from the 
tradition of the intelligent, the latter manifesting the universal 
through the light of the individual." (Pacii, p. 413. See the rest of 
the chapter). 

An. Pus., L. i. c. 18, § 1. — "But it is manifest that, if 
any sense be wanting, some relative science should be wanting 
likewise, this it being now impossible for us to apprehend. For 
we learn everything either by induction or by demonstration. 
Now, demonstration is from universals, and induction from parti- 
culars ; but it is impossible to speculate the universal unless 
through induction, seeing that even the products of abstraction 
will become known to us by induction." 



APPENDIX. 



361 



A. Aristotle's Errors regardiiio- Induction. 

Not making Syllogism and its theory superior and common to 
both Deductive and Inductive reasonings, 

A corollary of the preceding is the reduction of the genus Syllo- 
gism to its species Deductive Syllogism, and the consequent con- 
tortion of Induction to Deduction. 

B. Omissions. 
Omission of negatives. 

Of both terms reciprocating. 

C. Ambiguities. 

Confusion of Individuals and Particular. See Scheibler, [Ojjera 
Logica, P. iii. De Pro})., c. vi., tit. 3, 5. — Ed.] 

Confasion or non-distinction of Major or Minor extremes. 



The subsequent observations are intended only to show out 
Aristotle's authentic opinion, which I hold to be substantially the 
true doctrine of Induction ; to expose the multiform errors of his 
expositors, and their tenth and ten times tenth repeaters, would be 
at once a tedious, superfluous, and invidious labour. I shall, first 
of all, give articulately the correlative syllogisms of Induction and 
Deduction which Aristotle had in his eye ; and shall employ the 
example which now stands in the Organon, for, though physio- 
logically false, it is, nevertheless, (as a supposition), valid, in illus- 
tration of the logical process. 



AEISTOTLES COEEELATIVE SYLLOGISMS. 



{a) Of Induction. 
All C {man, liorse, mule, &c.) is 

some A {lonfj-lived) ; 
All G {man, horse, mule, &c.) is 

alt B {ivantiny-hile) ; 
AW^ {luanting-hile) is some A 

{long-lived). 



(6) Of Deduction. 
All^ {wanting-hile) is some A 

{long-lived) ; 
AUG {inan, horse, mule, &c.) is 

all B {wanting-hile) ; 
All G {man, horse, mule, &c.) is 

some A {long-lived). 



A, 



C(p,q,r,&c.): — :B A, 



B: 



; C (p, q, r, &c.) 



362 APPENDIX. 

These syllogisms, tliongli of different figures, fall in the same 
mood ; in our table they are of the eighth mood of the third and 
first Figures. Both imallowed. (See Ramus, quoted below, p. 363). 

The Inductive syllogism in the first figure given by Schegkius, 
Pacius, the Jesuits of Coimbra, and a host of subsequent repeaters, 
is altogether incompetent, so far as meant for Aristotle's correla- 
tive to his Inductive syllogism in the third. Neither directly nor 
indirectly does the philosopher refer to any Inductive reasoning 
in any other figure than the third. And he is right ; for the third 
is the figure in which all the inferences of Induction naturally 
run. To reduce such reasonino;s to the first figure, far more to the 
second, is felt as a contortion, as will be found from the two fol- 
lowing instances, the one of which is Aristotle's example of In- 
duction, reduced by Pacius to the first figure, and the other the 
same example reduced by me to the second. I have taken care 
also to state articulately what are distinctly thought, — the quanti- 
fications of the predicate in this reasoning, ignored by Pacius and 
logicians in general, and admitted only on compulsion, among 
others, by Derodon, (below, p. 363), and the Coimbra commen- 
tator." 

Aristotle's inductive syllogism in piciuees. 

(c). Fig. I. (J). Fig. II. 

All G {man, horse, mule, <fec.) is Some A {long-lived) is all G 

some A {long-lived) ; {jnan, horse, mule, &c.) ; 

All ^ (wanting -bile) is all G All H {ivanting-hile) is all G 

{man, horse, mule, &c.) / {man, horse, mule, &c.) ; 

All B {luanling-hile) is some A All B {wanting-hile) is some A 

{long-lived). {long-lived). 



II. — Pachymeres. 

Pachymercs, Epitome of Aristotle s Logic, (Title viii. cli. 3, 
c. 1280). — " Induction, too, is celebrated as another instrument 
of philosophy. It is more persuasive than Deductive reasoning ; 
for it proposes to infer the universal from singulars, and, if 
possible, from all. But as this is frequently impossible, indivi- 

o [In An. Prior., L. ii. p. 403. Cf. (1544). Tosca, Conip. Phil. Logica, t. 
Perionius, Dialect ira, L. iii. p. 356 I. 1. iii. c. 1, p. 115.] 



APPENDIX. 363 

duals being often in number infinite, there has been found a 
method through which we may accomplish an Induction, from 
the observation even of a few. For, after enumerating as many 
as we can, we are entitled to call on our adversary to state on 
his part, and to prove, any opposing instances. Should he do 
this, then [for, ' data instantia, cadit inductio'] he prevails ; but 
should he not, then do we succeed in our Induction. But Induction 
is brought to bear in the third figure ; for in this figure is it origi- 
nally cast. Should, then, the minor premise be converted, so that 
the middle be now predicated of all the minor extremes, as that 
extreme was predicated of all the middle ; in that case, the con- 
clusion will be, not of some, but of all. [In induction] the first 
figure, therefore, arises from conversion, — from conversion of the 
minor premise, — and this, too, converted into all, and not into 
so)ne. But [an inductive syllogism] is drawn in the third figure, 
as follows : — Let it be supposed that we wish to prove, — every 
animal moves the lower jaiu. With that intent, we place as 
terms : — the major, moves the under jaw ; the minor, \all\ ani- 
mal ; and, lastly, the middle, all contained under animal, so that 
these contents reciprocate with all animal. And it is thus perfected 
[?] in the first figure, as follows : — To move the lower jaw is predi- 
cated of all individual animals ; these all are predicated of all 
animcd; therefore, moving the lower jccw is predicated of all ani- 
mal. In such sort induction is accomplished." 

III. — Eamus. 

Ramus, Schoke Dialecticce, L. viii. c. 11. "Quid vero sit in- 
ductio perobscure [Aristoteli] declaratur: nee ab interpretibusintel- 
ligitur, quo modo syllogismus per medium concludat majus extre- 
mum de minore: inductio majus de medio per minus." Ramus has 
confirmed his doctrine by his example. For, in his expositions, he 
himself is not correct. 

IV. — Deeodon. 

Derodon, Logica Bestituta, 1659, p. 602. Philosophia Con- 
tracta, 1661', Logica, p. 91. "Induction is the argumentation in 
which, from all the particulars, their universal is inferred ; as — 
Fire, air, water, earth, are bodies ; therefore, every element 



364 APPENDIX. 

is hody. It is recalled, however, to syllogism, by assuming all 
the particulars [including singulars] for the middle term, in this 
manner : — Fire, air, water, and ea7'th are bodies ; hut fire, air, 
water, and earth are every element ; therefore, every element is 
hody. Again : — The head, chest, feet, cfcc, are diseased ; hut 
the head, chest, feet, <&c., are the whole animal ; therefore, the 
ivhole animal is diseased. Thus Induction is accomplished, when, 
by the enmneration of all the individuals, we conclude of the 
species what holds of all its individuals ; as — Peter, Paul, James, 
&c., are rational; thej^efore, all man is rational; orwhen, by the 
enumeration of all the sj)ecies, we conclude of the genus what holds 
of all its species; as — Man, ass, horse, d'C, are sensitive; there- 
fore, all animal is sensitive ; or when, by the enumeration of all 
the parts, we conclude the same of the whole ; as — Head, chest, 
feet, &c., are diseased ; therefore, the whole animal is diseased." 

v.— The College of Alcala. 

A curious error in regard to the contrast of the Inductive and 
the Deductive syllogism stands in the celebrated Cursus Complu- 
tensis, — in the Disputations on Aristotle's Dialectic, by the Car- 
melite College of Alcala, 1624, (L. iii. c. 2). We there find sur- 
rendered Aristotle's distinctions as accidental. Induction and 
Deduction are recognised, each as both ascending and descending, 
as both from, and to, the whole ; the essential difference between 
the processes being taken, in the existence of a middle term for 
Deduction, in its non-existence for Induction. The following is 
given as an example of the descending syllogism of Induction : — 
All men are animals; therefore, this, and this, and this, etc., man 
is an animal. An ascending Inductive syllogism is obtained from 
the i^receding, if reversed. Now all this is a mistake. The syllo- 
gism here stated is Deductive ; the middle, minor, and major 
terms, the minor premise and the conclusion being confounded 
together. Expressed as it ought to be, the syllogism is as follows : — 
All men are {some) animals ; this, and this, and this, cC'c, are 
(constitute) all men; thei-efore, this, and this, and this, d:c., are 
{some) animal. Here the middle term and three propositions re- 
appear ; whilst the Deductive syllogism in the first figure yields, of 
course, on its reversal, an Inductive syllogism in the third. 



APPENDIX. 365 

The vulgar errors, those till latterly, at least, prevalent in this 
country, — that Induction is a syllogism in the Mood Barbara of 
the first figure, (with the minor or the major premise usually sup- 
pressed) ; and still more that from a some in the antecedent, we 
can logically induce an all in the conclusion ; — these, on their own 
account, are errors now hardly deserving of notice, and have been 
already sufficiently exposed by me, upon another occasion, (Edin- 
burgh Review, LVII. p. 224 et seq.) [Discussions, p. 158 et seq. 
—Ed.] 

VI. — Facciolati. 

Facciolati, Rudimenta Logica, P. iii. c. 3, defines Induction 
as " a reasoning without a middle, and concluding the universal 
by an enumeration of the singulars of which it is made up." His 
examples show that he took it for an Enthymeme. — " Prudence, 
Temperance, Fortitude, &c., are good habits, [tJiese constitute all 
virtue] ; therefore, [(dl] virtue is a habit." 



VII. — Lambert. 

Lambert, Neues Organon, i. § 287. "When, in consequence of 
finding a certain attribute in all things or cases which pertain to a 
class or species [genus (?)], we are led to affirm this attribute of 
the notion of the class or genus ; we are said to find the attribute 
of a class or genus through induction. There is no doubt that 
this succeeds, so soon as the induction is complete, or so soon as we 
have ascertamed that the class or species A contains under it no 

other cases than C, D, E, F, M, and that the attribute B occurs 

in each of the cases C, D, E, F, M. This process now pre- 
sents a formal syllogism in Caspida. For we thus reason — • 

C, as well as T>, E, F, M are allB; 

But A is either C, or D, or E, or F or M ; 

Consequently, all A are B. 

"The example previously given of the syllogistic mood Gas- 
pida, may here serve for illustration. For, to find whether every 
syllogism of the Second Figure be negative, we go through its seve- 
ral moods. These are Cesare, Gamestres, Festino, Baroco. Now 



36C APPENDIX. 

both the first conclude in E, both the last in O. But E and are 
negative, consequently all the four, and herewith the Second Figure 
in general, conclude negatively.a As, in most cases, it is very diffi- 
cult to render the minor proposition, which has the disjunctive 
predicate for its middle term, complete, there are, therefore, com- 
petent very few perfect inductions. The imperfect are [logically] 
worthless, since it is not in every case allowable to argue from 
so7ne to all. And even the perfect we eschew, whensoever the 
conclusion can be deduced immediately from the notion of the 
genus, for this inference is a shorter and more beautiful." 

Strictures on Lambert's doctrine of Induction. 

1°, In making the minor proposition disjunctive. 

2°, In making it particular. 

3°, In making it a minor of the First Figure instead of the 
Third. 

Better a categorical syllogism of the Third Figure, like Aris- 
totle, whom he does not seem to have been aware of. Eefuted by 
his own doctrine in § 230. 

The recent German Logicians,(3 following Lambert, {N. Org. 
i. § 287), make the inductive syllogism a byeword. Lambert's 

example: — "C, as well as D, E, F M, all are B; but A 

is either C, ur D, or E, or F, or M ; thei^efore, all A is B." 

Or, to adapt it to Aristotle's example : — Man, as well as horse, 
mule, &c., all are long-lived animals ; hut animal void of gall is 
either man, or horse, or mule, &c. ; therefore, all animal void of 
gall is long-lived. 

This, I find, was an old opinion ; and is well invalidated by the 
commentators of Louvain.7 

a. It is given in § 285, as follows :— that the singulars in the Inductive syllo- 

" The syllogisms, as tvell in Cesare as in gism should be enumerated by a disjuuc- 

Camestres, Festino, and Baroco, are all tive conjunction, in so much that the 

negative; premises of such a syllogism are com- 

'' Now every syllogism of the Second monly wont to be thus cast: — What- 

Figiore is either in Cesare, or Camestres, soever is John, or Peter, or Paid, dx., is 

or Festino, or Baroco; cajmhle of instruction. But they err, 

"Consequently every syllogism in the not observing that the previous proposi- 

Second Figure is negative." tion is manifestly equivalent to the fol- 

/3 As Herbart, Lehrhuch der Logik, § lowing, — John, and Peter, and Paid, 

69. Twesten, Drobisch, II. Ritter. dr., are capable of instruction" (Lo- 

7 " I am aware of the opinion of many, vnnienses. Com. In An. Pr., L. ii. tr. 



APPENDIX. 367 

The only inducement to the disjunctive form is, that the predicate 
is exhausted without the predesignation of universality, and the 
'First Figure attained. But as these crotchets have been here 
refuted, therefore, the more natural, &c. 

Some logicians, as Oxford Crakanthorpe, {Logica, 1. iii., c. 20, 
published 1622, but written long before), hold that Induction can 
only be recalled to a Hypothetical syllogism. As, — If Sophocles 
he risible, likewise Plato and all other men, then all man is insihle; 
hut Socrates is risible, likewise Plato and all other men; thei-efore, 
all man is risible. Against the Categorical syllogism in one or 
other figure he argues : — "This is not a universal categorical, because 
both the premises are singular ; nor a singular categorical, because 
the conclusion is universal." It is sufficient to say, that, though 
the subjects of the premises be singular, (Crakanthorpe does 
not contemplate their being particular), as supposed to be all the 
constituents of a species or relatively universal whole, they are 
equivalent to that species ; their universality, (though contrary to 
Aristotle's canon), is, indeed, overtly declared, in one of the pre- 
mises, by the universal predesignation of the iwedicate. Our 
author further adds, that Induction cannot be a categorical syl- 
logism, because it contains four terms ; this quaternity being 



3, c. 2, p. 286, ed. 1547 ; 1st ed., All that is Socrates, or Plato, {and so 

1555). This here said of the major of others), runs ; hut all man is Socrates, 

is true of Lambert's minor. The Lou- or Plato, {and so of others) ; therefore, all 

vain masters refer probably [to Ver- 'nmn runs. And these singulars ought 

sor, &c.] This doctrine, — that the to be taken disjunctively, and disjunc- 

Inductive syllogism should be drawn tively, not computatively, verified of 

in a disjunctive form, — was commonly their universal " — {In. Hisp. Summul, 

held, esijecially by the scholastic com- Tr. v.) 

mentators on Petrus Hispauus. Thus The same doctrine is held in the Re- 
Versor, (to take the books at hand), ■parationes of Arnoldus de Tuugeri and 
whose £'.iyws/<«o?i first appeared in 1487, the Masters Regent in the Burse (or 
says — " In the fourth place. Induction College) of St Lawrence, in Cologne, 
is thus reduced to syllogism, seeing that, 1496. (Tr. iii., c. ii., Sec. Pri.) 
in the conclusion of the Induction, there It is also maintained in the Copulata 
are two terms of which the subject forms of Lambertus de Monte, and the other 
the minor, and the predicate the major. Regents in the Bui-sa Montis of Cologne, 
extreme in the syllogism ; whilst the 1490. They give their reasons, which 
singulars, which have no place in the are, however, not worth stating and re- 
conclusion, constitute the middle term, futiug. 

Thus the Induction — Socrates runs. But Tartaretus, neither in his Com- 

Plato runs, {and so of other men) ; there- mentaries on Hispanus nor on Aris- 

fore, all man runs,—\s, thus reduced : totle, mentions this doctrine. 



368 APPENDIX. 

made by the " all men," (in his example), of the premises being 
considered as different from the "all man" of the conclusion. 
This is the veriest trifling. The difference is wholly factitious : 
all man, all men, &c., are virtually the same ; and we may in- 
differently use either or both, in premises and conclusion. 

(h) Mateeial Induction. 

Material or Philosophical Induction is not so simple as com- 
monly stated, but consists of two syllogisms, and two deductive 
syllogisms, and one an Epicheirema. Thus : — 

I. — What is found true of some constituents of a natural class, 
is to he 'presumed true of the tvhole class, {for nature is always 
uniform) ; a a a' are some constituents of the class A ; therefore, 
ivhat is true of a a a" is to he presumed true of A. 

II. — What is true of a a a" is to he presumed true of A; 
hut z is time of a a' a" ; therefore, z is true <f A. 

It will be observed, that aU that is here inferred is only a pre- 
sumjotion, founded, 1°, On the supposed uniformity of nature ; 
2°, That A is a natural class ; 3°, On the truth of the observation 
that a a a" are really constituents of that class A ; and, 4°, That 
z is an essential quality, and not an accidental. If any be false, 
the reasoning is naught, and, in regard to the second, a a' a," (some)^ 
cannot represent A, (all), if in any instance it is found untrue. 
"Data instantia cadit inductio." In that case the syllogism has 
an undistributed middle. 



APPENDIX. 



309 



VIII. 



HYPOTHETICAL AND DISJUNCTIVE EEASONING— 
IMMEDIATE INFERENCE. 

A.— AUTHOR'S DOCTRINE— FRAGMENTS. 
(See above, Vol. I. p. 326.) 



All Mediate inference is one ; that 
cal ; for the Conjunctive and Disjun 
reasoning are reducible to immediate 



incorrectly called Categori- 
ctive forms of Hypothetical 
inferences. 









Immediate ; 

of which some 

kinds are 



Recognised, 

as Prepositional. 

(Various.) 



Not recognised, 
as Syllogistic, 



Mediate ; 

Syllogism Proper, 

(Categorical.) 



A) Analytic. 



B) Synthetic. 



Disjunctive, 

Conjunctive, 

a) Unfigured. 

\ b) Figured, 
(Intensive 
or Exten- 
sive) in 



Hypo- 
thetical. 



F. I. 
F. II. 
F. III. 



to M 



§ 1. Reasoning is the showing out explicitly that a proposition, 
not granted or supposed, is implicitly contained in something 
different, which is granted or supposed. 

§ 2. What is granted or supposed is either a single proposition, 
or more tlian a single proposition. The Reasoning, in the former 
case, is Immediate, in the latter, Mediate. 

§ 3. The proposition implicitly contained, may be stated first 
or last. The Reasoning, in the former case, is Analytic, in the 
latter, Synthetic. 

Observations. — § 1. "A proposition," not a truth ; for the pro- 
position may not, absolutely considered, be true, but relatively 
to what is supposed its evolution, is and must be necessary, 
All Reasoning is thus hypothetical ; hj^pothetically true, 



a Reprinted from Discussions, p. 65G. — Ed. 



VOI,. II. 



2 A 



870 APPENDIX. 

though absolutely what contains, and, consequently, what is 
contained, may be false." 

Observations. — § 2. Examples : Immediate — If A is B, then 
a is A; Mediate — If A is B, cmd B is C, then A is C. 

Observations. — § 3. Examples : Analytic — B is A, for A ts B ; 
A is C, for A is B, and B is C. Synthetic — A is B ; there- 
fore, B is A ; A is B, and B is C ; therefore, A is C. 

On the Nature and Divisions of Inference or Syllogism 

in general. 

(November 1848.) 

I. Inference, what 

II. Inference is of three kinds ; what I would call the — 1°, Com- 
mutative ; 2°, Explicative ; and, 3°, Comparative. 

1°, In the first, one proposition is given ; and required what are 
its formal commutations ? 

2°, In the second, two or more connected propositions are given, 
under certain conditions, (therefore, all its species are conditionals) ; 
and required what are the formal results into which they may be 
explicated. Of this genus there are two species, — the one the Dis- 
junctive Conditional, the other the Conjunctive Conditional. In 
the Disjunctive, (the Disjunctive also of the Logicians), two or 
more proj^ositions, with identical subjects or predicates, are given, 
under the disjunctive condition of a counter quality, i. e. that 
one only shall be affirmative ; and it is required what is the 
result in case of one or other being affirmed, or one or more denied. 
(Excluded Middle.) In the Conjunctive, (the Hypotheticals of 
the logicians), two or more propositions, convertible or contradic- 
tory, with undetermined quality, are given, under the conjunctive 
condition of a correlative quality, i. e. that the affirmation or 

a. That all logical reasoning is hypo- consequentice and iiccessitas consequent-is, 

thetical, and that Categorical Syllogism see Scotus, Qua'stiones, Super Elenchos, 

is really, and in a higher signification, qu. iv., p. 227, ed. 1639, and that all 

hypothetical, see Maimon, Versuch einer inference hypothetical, In An. Prior., 

ncuen Logik, § vi. l.jp-p. 82,88. E. Rein- L. ii. qu. i. p. 331. Apuleius, Z>e i7a6. 

hold, Loffik, § 109, p. 253 et seq. Smig- Doct. Plat., p. 34. Aristotle, .4 w. Prior, 

lecius, Zor//ca, Disp. xiii., q. 5, p. 495, (1st i. 32, § 5. Smiglecius, Logica, loc. cit. 

ed. 1616). Balforeus, In Arist. Org., An. Prior., i., 

On the nature of the Necessity in Syl- t. 8, p. 454, 1616. [See also Discussions, 

logisticlnference; distinction of Formal p. 146, note.— Ed.] 
and Material Necessity, or of necessitas 



APPENDIX. 371 

negation of one being determined, determines the corresponding 
affirmation or negation of the other or others ; and it is required 
what is the result in the various possible cases. (Identity and 
Contradiction, not Sufficient Keason, which in Logic is null as a 
separate law). 

8°, In the third, three terms are given, two or one of which are 
positively related to the third, and required what are the relations 
of these two terms to each other? "" 

III. All inference is hypothetical. 

IV. It has been a matter of dispute among logicians whether 
the class which I call Explicative, (viz. the Hypothetical and Dis- 
junctive Syllogisms), be of Mediate or Immediate inference. The 
immense majority hold them to be mediate ; a small minority, of 
which I recollect only the names of Kant, [Fischer, Weiss, Bouter- 
wek, Herbart],^ hold them to be immediate. 

The dispute is solved by a distinction. Categorical Inference is 
mediate, the medium of conclusion being a term ; the Hy])othetical 
and Disjunctive syllogisms are mediate, the medium of conclusion 
being a proposition, — that which I call the Explication. So far 
they both agree in being mediate, but they differ in four points. 
The first, that the medium of the Comparative syllogism is a term ; 
of the Explicative a proposition. The second, that the medium of 
the Comparative is one ; of the Explicative more than one. The 
third, that in the Comparative the medium is always the same; in 
the Explicative, it varies according to the various conclusion. The 
fourth, that in the Comparative the medium never enters the con- 
clusion ; whereas, in the Explicative, the same proposition is reci- 
procally medium or conclusion. 

V. Logicians, in general, have held the Explicative class to be 
composite syllogisms, as compared with the Categoric ; whilst a 

« A better statement of the three dif- third; — what are the inferences afforded 

f erent processes of Reasoning. in the relations to each other, which this 

I. Given a proposition ; commutative ; comparison of the two notions to the 
— what are the infei'ences which its com- third determines? 

mutations afford ? [;8 Kant, Logik, § 75. Bouterwek, 

II. Given two or more propositions ; Lehrhuch der philosopMscJien Vorlcennt- 
related and conditionally; — what are «/s6r, § 100, p. 158, 2d ed. 1820. Fischer, 
the inferences which the relative pro- Loyik, c. v. §§ 99, 100, p. 137. Weiss, 
positions, explicated under these con- Logik, §§ 210, 251. Herbart, Lehrhuch 
ditions, afford ? zur Eiiileituny in die Philosoj;)hie, § 64, 

III. Given three notions ; two re- p. 87, 1834.] 
lated, and at least one positively, to a 



372 APPENDIX. 

few have held them to be more simple. This dispute arises from 
each party taking a partial or one-sided view of the two classes. 
In one point of view, the Explicative are the more complex, the 
Comparative the more simple. In another point of view, the 
reverse holds good. 



Our Hypothetical and Disjunctive Syllogisms may be reduced 
to the class of Exj^licative or Conditional. The Hypotheticals 
should be called, as they were by Boethius and others. Con- 
junctive, in contrast to the co-ordinate species of Disjunctive. 
Hypothetical, as a name of the species, ought to be abandoned. 

The Conjunctives are conditional, inasmuch as negation or affir- 
mation is not absolutely asserted, but left alternative, and the quality 
of one proposition is made dependent on another. They are, how- 
ever, not jjroperly stated. The first proposition, — that contain- 
ing the condition, — which I would call the Explicand, should be 
thus enounced : J.s B, so A ; — or, As^ is, so is A ; or. As C is 
B, so is B A. Then follows the proposition containing the expli- 
cation, which I would call the Explicative ; and, finally, the 
proposition embodying the result, which I would call the Ex- 
ptlicate. 

They are called Conjunctives from their conjoining two con- 
vertible propositions in a mutual dependence, of which either may 
be made antecedent or consequent of the other. 

Disjunctive Syllogisms are conditional, inasmuch as a notion is 
not absolutely asserted as subject or predicate of another or others, 
but alternatively conjoined with some part, but only with some 
part, of a given plurality of notions, the affirmation of it with one 
part involving its negation with the others. The first proposition, 
containing the condition, I would call the Explicand, and so forth 
as in the Conjunctives. They are properly called Disjunctives. 

DlSTPJBUTION OP EeASONINGS. 

(Nov. 1848.) — Inference maybe thus distributed, and more fully 
and accurately than I have seen. It is either, (I.) Immediate, that 
is, without a middle term or medium of comj)arison ; or (II.) Me- 
diate, with such a medium.a 

a [Cf. Fonseca, Instit. Dial., L. vi. PMlosophice Quadripartita, Dialecflra, 
c. 1., 1st ed. 15G4. Eustachius, ,?(«««(* P. iii. tract, i., p. 112. [" Quoniam 



APPENDIX. 373 

Both the Immediate and the Mediate are subdivided, inasmuch 
as the reasoning is determined (A) to one, or (B) to one or other, 
conclusion. (It is manifest that this latter division may constitute 
the principal, and that immediate and mediate may constitute 
subaltern classes.) 

All inference, I may observe in the outset, is hypothetic, and 
what have been called Hypothetical Syllogisms are not more hypo- 
thetic than others. 

I. A — Immediate Peremptory Inference, determined one con- 
clusion, contains under it the following species : — a 

I. B — Immediate Alternative Inference contains under it these 
five species, — 

1°, Given one proposition, the alternative of aflSrmation and nega- 
tion. As — A either is or is not ; hut A is ; therefore A is not not. 
Or, A is or is not B ; but A is B ; therefore, A is not not-B. 

This species is anonymous, having been ignored by the logi- 
cians; but it requires to be taken into account to explain the 
various steps of the process. 

2°, Given one proposition, the alternative between different pre- 
dicates. This is the common Disjunctive Syllogism. 

argumentatio est quasdam consequentia, secutione, p. 492 et seq.'\ 
(latius enim patet consequentia quam o [Kinds of Immediate Inference. — 

ai-gumentatio), prius de consequentia, I. Subalternation. II. Conversion. III. 

quam de argumentatione dicendum est. Opposition — (a) of Contradiction — (b)of 

Consequentia igitur, sive consecutio, est Contrariety — (c) of Subcontrariety. IV. 

oratio in qua ex aliqiio aliquid colligitur ; Equipollence. V. Modality. VI. Con- 

ut, Omnis homo est animal, igitur aliquis traposition. VII. Correlation. VIII. 

homo est animal."- — Ed.] [Whether Im- Identity. 

mediate Inference really immediate, see, Fonseca (IV), (I), (II). Eustachius (I), 

on the affirmative, E. Reinhold, Logil; (IV), (II), (VIII). Wolf, (IV), (VII), 

§106; on the negative, Wolf, P/t(7.i?rt<., (Ill), a, b, c, (II). Stattler, (I), (IV), 

§ 461. Krug, Lof/lh, § 94, p. 287. (ID, (III). Kant, (I), (III), a, b, c), (II), 

Schulze, Logik, §§ 85-90, (§ 80, 5th ed.). (VI). E. Reinhold, (I), (II), (VI), (VII). 

Cf. Maimon, Versuch einer neuen Logil; Rosling, (I), (IV), (II), (III), a, b, c, (V), 

Sect. V. § 2, p. 74 et seq. F. Fischer, Krug, (IV), (I), (III), a, b, c, (II), (V). 

Logik, p. 104 et seq. Bachmann, Logik, G. E. Schulze, (IV), (I), (III), (II). S. 

§ 105, p. 154 et seq. Reimarus, Ver- Maimon, (I), (III), (II), (VI). Bachmann, 

7iimftlehre,%159 et seq. (1765). Bolzano, (IV), (I), (III), a, b, c, (II), (VI), (V). 

Wissenschaftslehre, Logik, vol. ii. § 255 Platner, (I), (II), (III), (IV). F. Fis- 

et seq. Twesten, Logik, inshesondere die cher, (V), (I), (III), (II), (VI). Reimarus, 

Analytik, § 77, p. 66. Rosling, Die IV., (I), (III), a, b, (II . Twesten, I), 

Lehren der reinen Logil; § 130, p. 391. (V), (III), (IV), (II), (VI). See above 

Scheibler, 0/3. Log., De Proposit. Con- pp. 283, 284.] 



374 APPENDIX. 

3°, The previous ji repositions conjoined, given one proposition, 
&c. As, A either is or is not either B or C or D; hut A is B ; 
therefore it is not not B, it is not C, it is not D. 

Alias, A is either B or non-'B, or C or non-G, or D or 7ion-D ; 
hut A isB; therefore it is not non-B, and it is non-C, and it is 
non-D. 

4", Given two propositions, second dependent on the first, and in 
the first the alternative of affirmation and negation. This is the 
Hypothetical Syllogism of the logicians. It is, however, no more 
hypothetical than any other form of reasoning ; the so-called 
hypothetical conjunction of the two radical propositions being 
only an elliptical form of stating the alternation in the one, and 
the dependence on that alternation in the other. For example, — 
If A is B, B is G ; this merely states that A either is or is not B, 
and that B is or is not C, according as A is or is not B. In 
short — As A is or is not B, so B is or is not 0. 

(Errors, — 1°, This is not a mediate inference. 

2°, This is not more composite than the categorical. 

3°, The second f)roposition is not more dependent upon the first, 
than the first upon the second.) 

5", Given two propositions, one alternative of affirmation and 
negation, and another of various predicates ; the Hypothetico- 
disjunctive or Dilemmatic Syllogism of the logicians. 

II. A — Mediate Peremptory Inference. This is the common 
Categorical Syllogism. Three propositions, three actual terms, 
one primary conclusion, or two convertible equally and conjunctly 
valid. 

II. B — Mediate Alternative Syllogism. Three propositions, 
three possible terms, and conclusions varying according .... 

2°, The Disjunctive Categorical. 

4°, The Hypothetical Categorical. 

5", Hypothetico-Disjunctive Categorical. 



Hypothetical Syllogism.— Canon. 

(Oct. 1848). — Canon — Two or more propositions thought as in- 
determined in quality, but as in quality mutually dependent, the 



APPENDIX. 375 

determination of quality in the one infers a determination of the 
corresponding quality in the other. 

This canon embodies and simpliiies the whole mystery of Hy- 
pothetical Syllogisms, which have been strangely implicated, muti- 
lated, and confused by the logicians. 

1°, What are called Hypothetical Propositions and Syllogisms 
are no more hypothetical than others. They are only hypothetical 
as elliptical. When we say, If A is, then B is, we mean to say 
the proposition, A is or is not, and the proposition, B is or is 
not, are mutually dependent, — that as the one so the other. If here 
only means taking for the nonce one of the qualities to the exclu- 
sion of the other; I, therefore, express in my notation the connec- 
tion of the antecedent and consequent of a hypothetical proposition, 
thus : — 

2°, The interdependent propositions are erroneously called Ante- 
cedent and Consequent. Either is antecedent, either is consequent, 
as we choose to make them. Neither is absolutely so. This error 
arose from not expressing overtly the quantity of the subject of the 
second proposition. For example, If man is, then animal is. In 
this proposition, as thus stated, the negation of the first does not 
infer the negation of the second. For man not existing, animal 
might be realised as a consequent of dor/, horse, &c. But let us 
consider what we mean ; we do not mean all animal, but so7ne 
only, and that some determined by the attribute of rational iti/ or 
such other. Now, this same some animal depends on man, and 
7nan on it ; expressing, therefore, what we mean in the proposition 
thus : — If all man is, then some animal is, — we then see the mutual 
dependence and convertibility of the two propositions." For to say 
that no animal is, is not to expKcate but to change the terms. 

3°, The interdependent propositions may be dependent through 
their counter qualities, and not merely through the same. For 
example, As our hemisphere is or is not illuminated, so the other 
is not or is ; hut the other is not illuminated; therefore ours is. 
Another, If A is, then B is not; hut B is; therefore A is not. 

<*■ Cf. Titius, Ars Cogltandi, c. xii. § lis, (1) iws'ito antecedente, ponitur conse- 

26. " In specie falsum quoque arbitror, qiiens, non vero remoto antecedente, re- 

quofl Syllogismi Conditionales duas ha- vioveturconsequens,{2)remotoco7}sequeiite, 

beaut figuras, quae his muuiantur i-egu- removetur antecedens, non autem posito 



376 



APPENDIX, 



Disjunctive and Hypothetical Syllogisms Proper. 

Aristotle ignores these forms, and he was right. '^ His followers, 
Theophrastus and Eudemus, with the Stoics, introduced them into 
Logic as coordinate with the regular syllogism ; and their views 
have been followed, with the addition of new errors, up to the pre- 
sent liour. In fact, all that has been said of them has been wrong. 

1°, These are not composite by contrast to the regular syllogism, 
but more simple. 

2°, If inferences at all, these are immediate and not mediate. 

8°, But they are not argumentations but preparations (explica- 
tions) for argumentation.^ They do not deal with the qufesitum, — 
do not settle it ; they only put the question in the state required 
for the syllogistic process ; this, indeed, they are frequently used 
to sujDcrsede, as placing the matter in a light which makes denial or 
doubt impossible ; and their own process is so evident that they 
might, except for the sake of a logical, an articulate, development 
of all the steps of thought, be safely omitted, as is the case with the 
qusesitum itself For example : — 



consequenfe, ponitur antecedens, . . 
§ 28. Videamus specialius ; contra 
primam regulam sic peccatur : 

Si Chhienses sunt Mahometan!, sunt 
infideles, 

At non sunt Mali.ometani, 

Ergo non sunt infideles, 

" nam conclusio hie est absurda ! Ve- 
rum si prsedicatum conclusionis sumatur 
particulariter, nulla est absurditas, si 
autem generaliter, turn evadunt quatuor 
termini. § 9. Eodem exemplo secunda 
regula etiam illustratur, sed assumemus 
aliud ex Weisio, d. I. 

Si miles est doctus, novit lihros (nempe 
eicut eruditi solent). 

Sed novit lihros (scil. ut alii homines, 
etiam indocti, nosse solent). 

Ergo miles est doctus. 

" Hsec conclusio itidem pro falsa habe- 
tur ! Sed jam indicavimus in addita 
parenthesi veram causam, nempe qua- 
tuor termino.s, quodsi autem medius 
terminus eodem sensu accipiatur, ac in 
syllogismo formaliter pi'oposito queat 
minor probari, tum conclusio erit veris- 



sima, idque virtute prscmissarum. § 30. 
Omnis igitur error exinde habet ori- 
ginem, quod quantitatem prsodicati vel 
non intelligant, vel non observent ; si 
igitur hunc lapsum evites, objecta ex- 
empla omnia, qualia etiam Weisius d. I. 
commemorat, facile dilues." — Ed. 

a Cf. Titius, Ars Cogitandi, c. xii. § 7. 
" SyllogismusDisjunctivus est en thyme- 
ma sine majore, bis, oratione disjuncta 
et positiva, propositum, . . . § 17. 
Conditionalis seu Hypotheticus nihil 
aliud est quam enthymema vel sine 
majore, vel minore, bis, prima scil. vice, 
conditionaliter, secunda, pure, proposi- 
tum. § 20. Sequitur nullum peculiare 
concludendi fundamentum vel formam 
circa Syllogismos Conditionales occur- 
rere, nam argumentationes imperfectas, 
adeoque materiam syllogismorum regu- 
larium illi continent." — Ed. 

/3 This I say, for, notwithstanding 
what M. St Hilaire so ably states in re- 
futation of my paradox, I must adhere 
to it as undisproved. — See his Transla- 
tion of the Organon, vol. iv., p. 55. 



APPENDIX. 877 

1. Hypothetical (so called) Syllogism. Let the qusesitum or pro- 
blem be, to take the simplest instance, — Does animal exist ? This 
question is thus hypothetically prepared — If man is, animal is. 
But [as is conceded] man is ; therefore, animal is. But here the 
question, though prepared, is not solved ; for the opponent may 
deny the consequent, admitting the antecedent. It, therefore, is 
incumbent to show that the existence of animal follows that of 
man, which is done by a categorical syllogism. 

Animal, '»— - — : Man -. m , Existent. 

2. Disjunctive (so called) Syllogism. Problem — Is John mortal? 
Disjunctive syllogism — John is either mortal or immortal ; hut 
he is not immortal ; ergo, [and this, consequently, is admitted as a 
necessary alternative], he is mortal. But the [alternative ante- 
cedent] may be denied, and the alternative consequent falls to the 
ground. It is, therefore, necessary to show either that he is not 
immortal, or, — the necessary alternative, — that he is mortal, which 
is done by categorical syllogism. 

John m^ , Man : »! : Immortal, 



John m» Man : ■— , Mortal. 



Hypothetical Infeeence. 

Inasmuch as a notion is thought, it is thought either as existing 
or as non-existing ; and it cannot be thought as existing unless it be 
thought to exist in this or that mode of being, which, consequently, 
affords it a ground, condition, or reason of existence. This is 
merely the law of Reason and Consequent ; and the hypothetical 
inference is only the limitation of a supposed notion to a certain 
mode of being, by which, if posited, its existence is affirmed ; if 
sublated, its existence is denied. For example, If A. is, it is B ; hut 
A is, &c. 

Again, we may think the existence of B (consequently of A B) 
as dependent upon C, and C as dependent upon D, and so forth. 
We, accordingly, may reason, //"A is B, and B is C, and C is D, &c. 

Disjunctive Syllogism People. 
(October 1848.) — Inasmuch as a notion is thought, it is thought 



378 APPENDIX. 

as determined by one or other, and only by one or other, of any 
two contradictory attributes ; and in as much as two notions are 
thought as contradictory, the one or the other, and only the one 
or the other, is thought as a determiniug attribute of any other 
notion. This is merely the law of Excluded Middle. The dis- 
junctive inference is the limitation of a subject notion to the one or 
to the other of two predicates, thought as contradictories ; the 
affirmation of the one inferring the negation of the other, and 
vice versa. As, A is either B or not B, &c. Though, for the 
sake of brevity, we say A is either B or C or D, each of these 
must be conceived as the contradictory of every other ; as, B = ] 
C I D, and so on with the others. 

Hypotheticals (Conjunctive and Disjunctive Syllogism). 
(April 30, 1849). — These syllogisms appear to be only modifica- 
tions or corruptions of certain immediate inferences ; for they have 
only two terms, and obtain a third proposition only by placing 
the general rule of inference, (stating, of course, the possible alter- 
natives,) disguised, it is true, as the major premise. It is manifest 
that we might prefix the general rule to every mediate inference ; 
in which case a syllogism would have four propositions ; or, at 
least, both j)reniises merged in one comj)lex j^roposition, thus — 

If A and he either subject or predicate, [of the same term ?] tliey are 

both subject or predicate of each other ; 
But B is the subject of A and predicate of B [C ?] ; 

.'. A is the jiredicate o/C-" 

Thus, also, a common hypothetical should have only two proposi- 
tions. Let us take the immediate inference, prefixing its rule, and 
we have, in all essentials, the cognate hyj)Othetical syllogism. 

] . — Conjunctive Hypothetical. 

Aim is {some or all) A ; All men are (some) animals ; 

Some or all B exists ; (All or some) men exist ; 

Therefore, some A exists. Therefore, some animals exist. 

a There seems to be an error here in hut B is A, and C is B; therefore, C is A. 

the author's M.S. It is obvious that a This is apparently what the author 

mediate inference may be expressed in means to express in a somewhat difFer- 

the form of a hypothetical syllogism, ent form. — Ed. 
Thus : // B is A, and C is B, then C is A; 



APPENDIX. 379 

Here it is evident that the first proposition merely contains the 
general rule, upon which all immediate inference of inclusion 
proceeds; to wit, that, the subjective part being, the subjective 
whole is, &c. 

Now, what is this but the Hj^othetical Conjunctive ? 

If B is, A is ; If man is, animal is ; 

But B is ; But man is ; 

Therefore, A is. Therefore, animal is. 

2. — Hypothetical Disjunctives. 

B is either A or not A ; Man is either animal or non- 

But B is A ; animal ; 

Therefore, B is not not- A. But man is animal ; 

Therefore, is not non-animal. 

Stating this hypothetically, we may, of course, resolve the for- 
mal contradictory into the material contrary. But this is wholly 
extralogical. 

Hypothetical and Disjunctive Syllogisms. 

(1848 or 1849.) — The whole antecedent must be granted ; and 
there cannot be two propositions inferred. In Categorical Syllo- 
gisms, the antecedent is composed of the major and minor premises, 
and there is only one simple conclusion, (though this may, in the 
second and thu-d figures, vary). So in Hypothetical and Disjunc- 
tive Syllogisms the whole antecedent is the two clauses of the 
first proposition ; and the whole inference is the first and second 
clauses of the second proposition, erroneously divided into minor 
proposition and conclusion. 

(January 1850.) — The Medium or Explicative may be indefinitely 
various, according to the complexity of the Explicand ; and so may 
the Explicate. The explicative and the explicate change places 
in different exjilications. There is, in fact, no proper medium- 
explicative or conclusion-explicate. 

(January 18.50.) — In Disjunctives there is always at least double 
the number of syllogisms (positive and negative) of the disjunct 
members ; and in all syllogisms where the disjunct members are 
above two, as there is thus afforded the possibility of disjunctive 



380 APPENDIX. 

explicates, there is another half to be added. Thus, if there be 
two disjunct members, as A — x B C, there are four syllogisms, 
but all of an absolute conclusion, — explicate. But if there be three 
disjunct members, as A — x B C D, in that case there are six 
absolute explicates, three positive and three negative, and, more- 
over, three disjunctivo-positive conclusions, — explicates, after a ne- 
gative explicative, and so on. 

HiTPOTHETICAL SYLLOGISM.— CaNONS. 

(February 1 850). — I. For Breadth, — The extensive whole or class 
being universally posited or sublated, every subjacent part is posited 
or sublated ; or for Depth, — All the comprehensive wholes being 
posited or sublated, the comprehended parts are universally posited 
or sublated. 

II. For Breadth, — Any subjacent part being posited or sublated, 
the extensive whole or class is partially posited or sublated ; or 
for Depth, — Any comprehensive whole being posited or sublated, 
the comprehended parts (or part) are, pro tanto, posited or sub- 
lated, — Conversion and Restriction. 

III. If one contradictory be posited or sublated, the other is 
sublated or posited, — Contradiction. 

IV. If some or a part only of a notion be posited or sublated, 
all the rest (all other some) is sublated or posited — Integration. 

V. If the same under one correlation be posited or sublated, so 
under the other, — Equipollence. 

VI. Law of Mediate Inference,« — Syllogism. 

Mem. — The some in the explicand is, (as in the Conversion of 
propositions), to be taken in the explicative as the same some. 
There is thus an inference equally from consequent to antecedent, 
as from antecedent to consequent.^ 

HYPOTHETICALS OR ALTERNATIVES. 

Conjunctive, (Hypotheticals emphatically), and Disjunctive, 
(Alternatives emphatically.) 

(August 1852.) 
Quantification, — A ny. 
Affirmative, — Any, {Anything, Aught), contams under it every 

a See above, p. 285.— Ed. j3 See above, p. 375. — Ed. 



APPENDIX. 381 

positive quantification, — All or Every, — Some at least, — Some 
only, — This, These. (Best.) 

Negative, — Not any, None, No, (Nothing, Naught), is equiva- 
lent to the most exclusive of the negations, All not; All, or every 
not; Not one, and goes beyond the following, which are only partial 
negations, — Not all; Not some; Some not. (Worst.) 

Affirmative, — Any, a highest genus and best ; not so Negative 
— Not any^ — a lowest species, and worst. Therefore can restrict, — 
subalternate in the former, not in the latter. 

1 2 



— Any, {all or every, — some). Some not, or not some, or not all- 

^ ~ 'ZT' r: ' some only, (def) 

rure ainrmative. v ": 



Mixed affirmative and negative. 

3 



All or every not, not one, not any. 
Pure negative. 

If any {every) M he an (some) A, and any {every) A an {some) S, then is 
any {every) M are S ; and v. v., if no {not any) A be any S, and any M 
some A, then is no M any S. 

.•. (On one alternative), some M bei7ig some A, and all A some S, some 
M is some S. 

(On the other), no A being any S, and every M so7ne A, no M is any S. 

If, (on any possibility), M is, some A is ; or, v. v., if no A is, no M is. 
.: (on one alternative), (in this actuality), some M being, some A is. 
on the other), 7io A being, noM is. 
Possible M : ,«-i — , A or A : ^ : M. Supposition of universal Pos- 

sibiUty. In any case. 
Actual M ,- » , A or A : » : A. Assertion of particular Actuality. 
In this case. 

From Possible, we can descend to Actual ; from Any, to Some ; 
but Not any being lowest or worst, we can go [no] lower. 

The Possible indifferent to Affirmation or Negation, it contains 
both implicitly. But when we descend to the Actual, (and Poten- 
tial ?), the two qualities emerge. This explains much in both 
kinds of Hypotheticals or Alternatives, — the Conjunctives and 
Disjunctives. 

Higher classes, — Possible, Actual — Semjyer, quandocunque, 
tunc, nunc — Ubicunque, ubique, ibi, hoc — Any, all, some, — In all, 
every, any, case, in this case — Conceivable, real. 



382 APrENDIX. 



EuLEs OF Hypothetical Syllogisms. 

1. Universal Rule of Restriction. — What is thought of all is 
thought of some, — what is thought of the whole higher notion, 
(genus), is thought of all and each of the lower notions, (special or 
individual). 

2. General Rule of both Hypotheticals. — What is thought (ira- 
plictly) of all, the Possible, (genus), is thought (explicitly) of all 
and each, the Actual, (species). 

3. Special Rule of Conjunctives. — What is thought as consequent 
on every Possible, is thought as consequent on every Actual, ante- 
cedent. 

4. Special Rule of Disjunctives. — What is thought as only Pos- 
sible, (alternatively), is thought as only Actual, (alternatively). 

5. Most Special Rule of Conjunctives 

6. Most Special Rule of Disjunctives 

Hypotheticals — Examples Unquantified. 

(Higher to Lower.) 
Affirmative. Negative. 

If the germs is, the species is. If the genus is not, the species is not. 

If the stronger can, the weaker can. If the stronger cannot, the weaker 

cannot. 

(Lower to Higher.) 

If the species is, the genus is. If the species is not, the gemis is not. 

If the weaker can, the stronger can. If the weaker cannot, the stronger 

cannot. 

(Equal to Equal.) 

If triangle, so trilateral. If A he father of B, B is son of A; 

iSicch poet Homer, such poet Virgil. .'. A heing father o/B, B is son of A ; 
Where {when) the carcase is, there .'. B not being sou of A, A is not 

{then) are the flies. father of B. 

If Socrates he the son of Sop>hronis- If the angles he proportional to the 
cus, Sop)hroniscus is the father sides of a A; 

of Socrates. .'. An equiangular tv ill be an equi- 

If equals he added to equals, the lateral A. 

wholes are equal. If wheresoever the carcase is, there 

will the eagles he gathered to- 
gether. (Matth. xxiv. 28). 
.'. If here the carcase is, here, &c. 



APPENDIX. 383 



A.) — Conjunctive Hypothetic als. 

1). // A he D, it is A ; .-. { f ^'''f ;D, is A; 

( A, not being A, **' ''O^ i) ; 
/m o^Aer words, A is ez'iAer D o?' not A D. 

Identity and Contradiction. 

2). // B 6e A, it is not non-k ■ .: \ ^' f^("^ ^' '"V^".^ ''""f ^ 

; B, being non-A, is not A ; 

In other words — B is either A or non-A. 
Excluded Middle. 

..\ rv-- -D 7 4 K .t • A } Vinotheinq A,isnon-A; 

3). 7/ B be not A, it is non-A ;..(,. . ■ . 

) B bemg non-A, is not A ; 

III other words — B is either not A or not non-A. 
Excluded Middle. 

4). //E he not D, it is not A ■ .: \ S' f^^ ^^f9\i^ '^«^ ^ J 

) E being A, is D ; 

In other ivords — E is either not D A, or A D. 
Contradiction and Identity. 



b).— Disjunctive Hypotheticals. 

// B he either A or non-A ■ .-. \ ^ ^''!'3 ^' *\^^? ^^'^f ' 

) B being non-A, is not A. 

Excluded Middle. 



" i/" means suppose that, — in case that, — on the supposition — 
— hypothesis — under the condition — under the thought that, — it 
being supposed possible ; 

.'. &c., means then, — therefore, — in that case, &c., &c. — in 
actuality eithei\ 

Only, properly, in botli Conjunctives and Disjunctives, two con- 
tradictory alternatives. Por contrary alternatives only material, 
not formal, and, in point of fact, either A or B or C means A or 
non-A., B or woh-B, C or non-C. 

The minor premise, on the common doctrine, a mere materi- 
ality. Formally, — logically, it is a mere differencing of the conclu- 
sion, which is by formal alternative aflbrded. 



384 APPENDIX. 

1.) In Hypotlieticals, (Conjunctive and Disjunctive), two or three 
hypotheses. The first is in the original supposition of possibi- 
lity. {If B be A, it is not non-A — If B be eitJie?' A or non-A). 
The second (and third) is in the alternative suppositions of actua- 
lity (.•. either if B be A, it is not non-A, or if B be non-A, it is 
not A. — .•. If B be A, it is not non-A, or if B be non-A, it is not 
A). (Possibly, — by possible supposition) If man is, animal is; 
.: (actually) Man being, animal is; (or) animal not being, man 
is not. 

1). Possibility — a genus indifferent to negative and affirmative. 
These two species of Possibility, to wit two Actuals, — an actual yes 
and an actual no. The total formal conclusion is, therefore, of 
two contradictories. This explains why, in Conjunctive and Dis- 
junctive Hypotheticals, there are two alternative consequents, and 
only one antecedent. 

2). In Hypotheticals (Conjunctive and Disjunctive) a division of 
genus in the first supposition into two contradictories, — species. 
The inference, therefore, one of subalternation or restriction. 

3). In Hypotheticals, (Conjunctive and Disjunctive), two alter- 
native contradictory conclusions — the form giving no preference 
between the two, the matter only determining, (other immediate 
inferences have only one determinate conclusion, and all mediate 
syllogism has virtually only one). Formally, therefore, we cannot 
categorically, determinately, assert, and assert exclusively, either 
alternative, and make a minor separate from the conclusion. This 
only materially possible ; for we know not, by the laws of thought, 
whether a certain alternative is, knowing only that one of two 
alternatives must be. Formally, therefore, only an immediate 
inference, and that alternative double. 

4). Hypothetical, (Conjunctive and Disjunctive), reasoning more 
marking out, — predetermining, how a thing is to be proved 
than proving it. 

5). Thus, three classes of inference : 1°, Simple Immediate In- 
ference. — 2°, Complex Immediate Inference, (Hypotheticals Con- 
junctive and Disjunctive). — 3°, Syllogisms Proper, Mediate Infer- 
ence. 

6). If we quantify the terms, even the formal inference breaks 
down. 

7). The only difference between the first proposition and the 



APPENDIX. 385 

two latter, is the restriction or subalternation. These last should, 
therefore, be reduced to one, and made a conclusion or restriction. 
The genera and species are of the most common and notorious 
kinds, as Possible and Actual, — Wherever, Here, &c. — Whenever, 
Noio, — All or Every, Some, This, &c. The commonness and noto- 
riety of this subordination is the cause why it has not been sig- 
nalised ; and if signalised, and overtly expressed, Hypotheticals 
might be turned into Categoricals. It is better, however, to leave 
them as immediate inferences. For it would be found awkward 
and round-about to oppose, for example, the Possible to the 
Actual, as determining a difference of terms. (See Molinseus, Mem. 
Log., L. i. tr. iii. p. 95, and Pacius, In Org., De 8yll. Hyp., p. 533.) 
The example of the Cadaver there given, shows the approximation 
to the ordinary Hypotheticals. They may stand, in fact, either for 
Categoricals or Hypotheticals. 

8). Disjunctives — (Possibly) A is cither B or non-'^ ; .'. (Actu- 
ally) A is cither, &c. 

9). The doctrine in regard to the Universal Quantity, and the 
Affirmative Quality (see Krug, Loejih, §§ 57, 83, 86, pp. 171, 264, 
275), of the supposition, proposition, of Conjunctive (?) and Dis- 
junctive Hypotheticals, is solved by my theory of Possibility. In 
it is virtually said, (whatever quantity and quality be the clauses) — 
" on any possible supposition." (On the Quality v. Krug, Logih, § 
57, p. 172. Pacius, In Org., p. 533. Molin?eus, Eleiii. Log., I. c.) 

10). Possibly, — problematically includes as species the actual 
affirmative, and the actual negative. It will thus be superfluous 
to enounce a negative in opposition to an affirmative alternative ; 
for thus the possible would be brought down to the actual ; and 
the whole syllogism be mere tautological repetition. 

11). The quantified terms, if introduced, must either be made 
determinate, to suit the Hj^otheticals, or must ruin their infer- 
ence. Por example — If all or some man be some animal, we 
must be able to say. But some animal is not, therefore man 
{any or some) is not. But here some animal, except definitised 
into the same some animal, would not warrant the required infer- 
ence. And so in regard to other quantifications, which the logicians 
have found it necessary to annul. 

12). The minor proposition may be either categorical or hypo- 
thetical. (See Kj-ug, Logik, § 83, p. 264. Heerebord, Instit. 

VOL. II. 2 B 



386 -APPENDIX. 

Logicar. Synopsis, L. ii. c. 12, pp. 266, 267.) In my way of stat- 
ing it : — If man is,- animal is, .: If man is (or ma7i being), 
animal is. 

13). Of notions in the relation of sub-and-superorclination, (as, 
in opposite ways Depth and Breadth, Containing and Contained), 
absolutely and relatively, the lower being affirmed, the higher are 
(partially) affirmed ; and the higher being (totally) denied, the 
lower are (totally) denied. A, E, I, O, U, Y may represent the 
descending series. 

The first proposition is conditional, complex, and alternative ; 
we should expect that the second should be so likewise. But this 
is only satisfied on my plan ; whereas, in the common, there is a 
second and a third, each categorical, simple, and determinate. 



The subalternation is frequently double, or even triple, to wit, 
1 °, From the Possible to the Actual. 2°, (for example) From every- 
where to hei'e, or this place, or the place by name. 3°, From all 
to some, &c. — in fact, this inference may be of various kinds. 

The [xeTaXr]\l/L<s of Aristotle may mean the determination, — the 
subalternation ; the Kara TroioTiqra may refer to the specification 
of a particular quality or proportion under the generic ; and the 
Trpoa\iq^i<i of Theophrastus (for the reading in Aristotle should 
be corrected) may correspond to the Kara TTOLOTTjTa. 



There is no necessary connection, formally considered, between 
the antecedent and consequent notions of the Hypothetical major. 
There is, consequently, no possibility of an abstract notation ; their 
dependence is merely supposed, if not material. Hence the logi- 
cal rule, — Propositio conditionalis nihil ponit in esse. (See Krug, 
Logik, § 57, p. 166.) But on the formal supposition, — on the case 
thought, what are the rules ? 



We should distinguish in Hypotheticals between a propositional 
antecedent and consequent, and a syllogistic A and C ; and each 
of the latter is one proposition, containing an A and C. 

The antecedent in an inference should be that which enables us 
formally to draw the conclusion. Show in Categoricals and in 
Immediate Inferences. On this principle, the conclusion in a 



APPENDIX. 887 

Hypothetical will contain what is commonly called the minor 
proposition with the conclusion proper ; but it will not be one and 
determinate, but alternative. 

If there were no alternation, the inference would follow imme- 
diately from the fundamental proposition ; and there being an al- 
ternative only makes the conclusion alternatively double, but does 
not make a mediate inference. 

To make one alternative determinate is extralogical ; for it is 
true only as materially proved. 1'^, The splitting, therefore, of the 
conclusive proposition into two, — a minor and a conclusion proper, 
is wholly material and extralogical ; so also, 2°, Is the multiply- 
ing of one reasoning into two, and the dividing between them of 
the alternative conclusion. 



Errors of logicians, touching Hypothetical and Disjunctive Rea- 
sonings : — 

1°, That [they] did [not] see they were mere immediate infer- 
ences. 

2°, Most moderns that both Hypothetical. 

3°, That both alternative reasonings in one syllogism. 

4°, Mistook a part of the alternative conclusion for a minor 
premise. 

5°, Made this a distinct part, (minor premise), by introducing 
material considerations into a theory of form. 

6°, Did not see what was the nature of the immediate inference 
in both, — how they resembled and how they differed. 

B.-HISTORICAL NOTICES. 

(Conjunctive and Disjunctive.) 

I. Aristotle. 

(August 1852.) 

Aristotle, {Anal. Pr. L. i. c. 32, § 5, p. 262, Pacii,) describes the 
process of the Hypothetic Syllogism, (that called by Alexander 
St' o\(ov), but denies it to be a syllogism. Therefore his syllogisms 
from Hypothesis are something different. This has not been no- 
ticed by Mansel, Waitz, 

Thus literally : — " Again, if man existing, it be necessary that 



388 APPENDIX. 

animal exist, and if animal, that substance ; man existing, it is 
necessary that substance exist. As yet, there is, however, no syl- 
logistic process ; for the propositions do not stand in the relation 
we have stated. But, in such like cases, we are deceived, by reason 
of the necessity of something resulting from what has been laid 
down ; whilst, at the same time, the syllogism is of things neces- 
sary. But the Necessary is more extensive than the Syllogism ; 
for though all syllogism be indeed necessary, all necessary is not 
syllogism." Why not? 1°, No middle. 2", No quality, — affirma- 
tion or negation ; problem, also not assertory, — hypothetical not 
syllogistic. 3°, No quantity. Compare also An. Pr. L. i. c. 24. 

Aristotle, {Anal Post, L. i. c. 2, § 15, p. 418 ; c. 10, §§ 8, 9, 
p. 438) makes Thesis or Position the genus opposed to Axiom, 
and containing under it, as species, \°, Hypothesis or Supposition ; 
and, 2°, Definition. Hypothesis is that thesis which assumes 
one or other alternative of a contradiction. Definition is that 
thesis which neither affirms nor denies. Hypothetical, in Aris- 
totle's sense, is thus that which affirms or denies one alternative 
or other, — which is not indifferent to yes or no, — which is not 
possibly either, and, consequently, includes both. Hypotheticals, 
as involving a positive and negative alternative, are thus, in Aris- 
totle's sense, rightly named, if divided ; but, in Aristotle's sense, 
as complete, they are neither propositions nor syllogisms, as not 
affirming one alternative to the exclusion of the other." 

II. — Ammonius Heemi^. 

I. Ammonius Hermiae, on Aristotle Of Enounceinent, Intro- 
duction, f 3. ed. Aid. 1546, f 1. ed. Aid. 1503. After distinguish- 
ing the five species of Speech, according to the Peripatetics, — 

o [Whether the Syllogisms ex Hypo- Tract. Si/ll. P. iv. c. x. tit. 2, p. 548. Burs- 

thesi of Aristotle are correapondent to gersdicius, Instit. Log. L. ii. cc. 12, 14, 

the ordinary Hypothetical Syllogism. pp. 263, 270, 275. Ritter, Gesch. der 

For the affirmative, see Pacius, Com. Phil. iii. p. 96. (Eng. Tr., p. 80), 
in Org. An. Prior., L. i. cc. 23, 29, 44, Ramus, Sckoke Dial. L. vii. cc. 12, 13, 
pp. 153, 177, 194, St Hilaire, Transla- pp. 492, 503. Molinasus, Elementa Lo- 
tion of Organon, vol. ii. pj). 107, 139, gica, p. 95 et seq. Waitz, Org. i. pp. 
178. 427,433. Ci. Alexander, In An. Prior., 

For the negative, see Piccartus, In S. 88, 109. Philoponus, In An. Prior., 

Org.An. Prior,h. I 00.40,4:1, 42, p. 5Q0. ff. 60'\ 60", 87", 88. Anonymus, Be 

Neldelius, Be Usu Org. Arist. P. iii. c. 2, Syllogismo, f. 44''. Magentinus, In An. 

pp. 38, 45., (1607.) Keckermanu, Opera, Prior., i. 17". Ammonius, In de Interp., 

pp. 766, 767. Scheibler, Oj^era Logica 3'\ Blemmidas, Epit. Log. c. 36.] 



APPENDIX. 889 

the Vocative, the Imperative, the Interrogative, the Optative, and 
the Enunciative or Assertive, — having further stated the corres- 
ponding division by the Stoics, and having finally shown that 
Aristotle, in this book, limited the discussion to the last kind, that 
alone being recipient of truth and falsehood, he thus proceeds : — 
"Again, oi Assertive speech, [aTTocfiavTLKOv \oyov), there are two 
species ; the one called Categoric [or Predicativel, the other 
Hypothetic [or Suppositive]. The Categoric denotes, that some- 
thing does or does not belong to something : as when we say, 
Socrates is walking, Socrates is not walking; for we predi- 
cate lualking of Socrates, sometimes affirmatively, sometimes nega- 
tively. The Hypothetic denotes, that something being, something 
[else] is or is not, or something not being, something [else] is 
not or is : As when we say, If man be, animal also is, — If he 
be man, he is not stone, — If it be not dag, it is night, — If it be 
not day, the sun has not risen. 

" The Categoric is the only species of Assertive speech treated 
of by Aristotle, as that alone perfect in itself, and of utility in 
demonstration ; whereas Hypothetic syllogisms, usurping [usually] 
without demonstration the [minor] proposition, called the Tran- 
sumption, or Assumption, and sometimes even a [major premise] 
Conjunctive or Disjunctive, requiring proof, draw their persuasion 
from hypotheses, should any one [I read et rtg for 17x1?,] con- 
cede their primary suppositions. If, then, to the establishment of 
such suppositions, we should employ a second hypothetic syllo- 
gism, — in that case, we should require a further establishment 
for confirmation of the suppositions involved in it ; for this 
third a fourth would again be necessary ; and so on to infinity, 
should we attempt by hypotheses to confirm hypotheses. But 
to render the demonstration complete and final, it is manifest 
that there is needed a categoric syllogism to prove the point in 
question, without any foregone supposition. Hence it is, that 
Categoric [reasonings] are styled Syllogisms absolutely ; whereas 
Hypothetic [reasonings] of every kind are always denominated 
Syllogisms from hypothesis, and never Syllogisms simply. Add 
to this, that Hypothetic enouncements are made up of Categoric. 
For they express the consequence or opposition [aKokovdiav rj 
Siacrracrti') of one Categoric proposition and another, uniting 
them with each other, by either the Conjunctive or Disjunctive par- 



390 APPENDIX. 

tide, {(TV[X7r\eKTLK(^ ^ Sta^evKxtKoi avvSeajxcp), in order to 
sliow that they constitute together a single enouncement. For 
these reasons, therefore, Aristotle has only considered, in detail, 
the Categoric species of Assertive speech." 

III. — Anonymous Scholion.'' 

In Hypothetic Syllogisms, the first [I] are those of two terms, 
[a] Conjunctive, or [b] Disjunctive, {opot ol avvrjixixevoL r) Sta- 
XeXv/xeVot) ; then follow [II] the two [classes of] syllogisms with 
three, and these conjunctive terms. 

[I. a]. " There are four syllogisms through the Return (17 ctt- 
dvoSos) on the prior (6 7rp6Tepo<i, 6 irpoiTO';) [or antecedent clause 
of the hypothetical proposition], and four through it on the pos- 
terior (6 ^evTepo^;, 6 ea^aTO'^). For the terms are taken, either both 
affirmatively or both negatively. And the return upon the prior is 
ponent {Kara Oiaiv) upon the posterior tollent [Kara avaipeaiv. 
For example [the return upon the prior] : — 

(1). If A is, B is ; (Return) but A is; {Conclusion, o-v/xirepaa-na) ikerefore, 
Bis. 

(2). If A is, B is not ; but A is ; therefore, B is not. 

(3). If A is not, B is ; hit A is not, therefore, B is. 

(4). If A is not, B is not : but A is not ; therefore, B is not, 

" The return upon the posterior : — 

(1). If A is, B is ; but B is 7iot ; therefore, A is not. 

(2). If A is, B is not ; but B is ; therefore, A is not. 

(3). If A is not, B is ; but B is not ; therefore, A is. 

(4). If A is not, B is not ; but B is ; therefore, A too is. 

[b.] " Following those of conjunctive, are syllogisms of disjunc- 
tive, terms. In these, the return is upon either [clause] indifferently. 
For example : If it must he that either A is or B is ; [in the one 
case], B is not, therefore, A is ; or, [in the other], A is not, there- 
fore B {5. 

[II.] " Of three conjunctive terms, there are [in the figures taken 
together] eight syllogisms, through a return on the prior, and eight 
[sixteen] P through a return on the posterior [clause]. For the 

a lu Waitz, Org. i., pp. 9, 10. placed first, according to the common 

jS It would seem that the author here, practice of the Greeks, or the major 

and in the last sentence, discounts alto- prior, in Aristotelic theory), he should 

gether the first figure, puzzled, appa- accord the designation of first, 
rently, to which premise, (the minor 



APPENDIX. 391 

three terms are correlated (o-vvTiOevTaC), either all affirmatively, 
or some ; and here either the third alone, or the third and second, 
or the second alone, negatively. Again, either all are negatively 
correlated, or some ; and here either the third alone, or the third 
and second, or the second alone, affirmatively. In this manner 
the correlation [in each figure] is eightfold ; taking for exemplifi- 
cation only a single mood [in the several figures] : — 

If A is, B is : 
7/'B is, C is ; 
If A is, there/ore, G is. 

This is of the first figure. Por the middle coUative term 
(6 (rvuayoju opo<^ fxecrog) is twice taken, being the consequent 
(6 XTJycou) in the former conjimctive [premise] {to irpoTcpov 
crvvr)fMjJieuop), the antecedent (6 -qyovixevoi) in the latter. Where- 
fore, these syllogisms are indemonstrable," not requiring reduction 
(t) avaXvcTLS;) for demonstration. The other moods of the first 
figure are, as has been said, similarly circumstanced. 

" The second figure is that in which the collative term [or 
middle] (6 crvpaycov) holds the same relation to each of the col- 
lated [or extreme] terms, inasmuch as it stands the antecedent of 
both the conjunctive [premises], except that in the one it is affirm- 
ative; in the other, negative. Wherefore, when reduced to the 
first figure, they demonstrate, as is seen, through the instance of a 
single mood composed of affirmative collated terms. As : — 

If A is, B is; 

If A is not, C is ; 

IfB is not, therefore, C is. 

" This is reduced to the first figure in the following manner : — 
"Whether it has the collated terms, both affirmative, or both nega- 
tive, or both dissimilar to the reciprocally placed collative term, 
there is taken in the reduction the opposite [and converse] of the 
prior conjunctive [premise] ; and the latter is applied, in order 
that the opposite of the consequent in the former conjunctive [pre- 
mise] may find a place in the foresaid mood. As : — 

If B is not, A is not ; 
If A is not, G is ; 
If'Bisnot,the7'efo7r,Gis. 

" This it behoved to show. 

» Vide Apuleius. [De. Dorjm. Plat. iii. p. 37. Elm. Cf. Discussions, -p. 836.— Ed.] 



392 APPENDIX. 

" The third figure is that in which the collative terra holds the 
same relation to each of the collated terms, being the consequent 
in either conjunctive [premise] afiirmatively and negatively, as in 
the example of a single mood again consisting of affirmative col- 
lated terms. Thus :— 

If A. is, B is ; 

7/C is, B is not ; 

If A. is, therefore, C is not. 

"The reduction of this to the first figure is thus effected. The 
opposite [a converse E] of the second conjunctive [premise] is 
taken along with the first conjunctive [premise], and the ante- 
cedent of the former is appHed to the opposite of the latter's con- 
sequent ; as in the foresaid mood. Thus : — 

If A is, B is ; 

IfB is, C is not ; 

If A is, therefore, C is not. 

" All this requires to be shown concretely. As in the first figure 
[first mood] : — 

If day is, light is ; 

If light is, visible objects are seen ; 

If day is, therefore, visible objects are seen. 

" Second figure, first mood : 

If day is, light is ; 

If day is not, the sun is under the earth ; 

If light is not, the sicn is [therefore], under the earth. 

" Eeduction : 

//' liffht is not, day is not ; 

If day is not, the sun is under the earth ; 

If light, therefore, is not, the sun is under the earth. 

" Third figure, first mood : 

If day is, light is ; 

If things visible are unseen, light is not ; 

If day, therefore, is, things visible are not tinseen. 

" There are eight moods of the second figure, and eight of the 
third ; two composed of affirmatives, two of negatives, four of dis- 
similars, with a similar or dissimilar collative. 

" End of Aristotle's Analytics." 



APPENDIX. 893 



Eelative to the translation from the Greek interpolator on 
Hypothetical Syllogisms, in Waitz, {Org. \., pp. 9, 10) ; and in 
particular to the beginning of [IL] 

Better thus : — In all the Figures : — the quality of the syllogism 
is either Pure, — and here two, viz., one affirmative and one nega- 
tive ; or Mixed, — and here six, viz., three in which affirmation, and 
three in which negation, has the preponderance. 

The following are thus arranged : — 

First Figure. Second Figure. Third Figure. 

' ^ All If A is, B is ; If B is, A is ; If A. is, B is ; 

p* A // B is, C is ; If B is, C is ; If C is, B is; 

fe .'. If K is, C is. .-. If A is, C is. .'. If A is, C is. 

a 

I 1,2 If A is, B is : If B is, A is ; If A is, B is ; 

S. B // B is, C is not ; If B is, C is not ; If C is not, B is ; 

"£ .'. If A is, C is not. .•. If A is, C is not. .'. If A is, C is not. 

& 

g 1> 3 If A is, B is not ; If B is not, A is ; If A is, B is not: 

•2 C IfB is not, C is ; If B is not, C is ; If C is, B is not ; 

g .'.If A is, C is. ,'. If A is, C is. .". If A is, C is. 

y^ 2,3 If A is not, B is ; If B is, A is not ; If A is not, Bis ; 

^ IfB is, C is J If B is, C is ; If C is, B is ; 

.•. If A is not, C is. .'. If A is not, C is. .'■ If A is not, C is. 



All If A is not, B is not. If B is not, A is not ; If A is not, B is not ; 

E If B is not, C is not ; If B is not, C is not ; If C is not, B is not ; 

.•. If A is not. C is not. .-. IfB is not, C is'not; •'■ If A is not, C is not. 

1)2 /y A is not, B is not ; If B is not, A is not. If A is not, B is not. 

F IfB is not, C is ; If B is not, C is ; If C is, B is not ; 

.: If A is not, C is. .-. // A is not, C is. •'■ If -^ is ^'of, C is. 

1 ' ^ If A is not, B is ; If B is, A is not ; Jf A is not, B is ; 

^ IfB is, C is not ; If B n, C is not ; If C is not, B is ; 

.•. If A is not, C is not. .'. If A is not, C is not. .-. If A is not, C is not. 



m 



2, 3 If A is, B is not ; 


IfB is not, A is; 


H IfB is not, C is not; 


IfB is not, C is not ; 


.: If A is, C is not. 


.'.If A is, C is not. 



^ 2, 3 // A is, B is not ; If B is not, A is ; If A is, B is not ; 

If C is not, B is not ; 
.: If A is, C is not. 

These eight syllogisms are all affirmative, the negation not being 
attached to the principal copula.* If, therefore, the negation be 

a See Lovanienses, In Arist. Dial, Tract, de Hypotheticis Syllogismis, p. 299. 



394 



APPENDIX. 



attached to one or other premise, there will be sixteen negative 
syllogisms, in all twenty-four. The negatives are, however, awk- 
ward and useless. — (See Lovanienses, p. 301.) 

But each of these twenty-four syllogisms can receive twelve, 
different forms of predesignation, corresponding to the twelve moods 
of the simple categorical ; according to which they are arranged 
and numbered. It is hardly necessary to notice that the order 
of the premises is in Comprehension, after the Greek fashion of the 
scholiast. 





i. 


ii. 


ill. 


iv. 


V. 


vi. 


vii. 


viii. 


ix. 


X. 


xi. 


xii. 




TA 




> 


J 


: 




> 




) 


> 


: 


> 


' 




MB 










> • 


• ) 


J • 


• 5 


> • 


• J 


} • 


• 5 




CC 




} 




> 


' 


•• 


> 


: 




> 


5 


> 





This is exemplified in the Syllogism E of the preceding table, 
thus : 

1. IfciJl A is not, all B is not ; if all B is not, all C is not ; .". if all A 

is not, all B is not, 

2. If some A is not, all B is not ; if all B is not, some C is not ; .'. if 

some A is not, someG is not. 

3. If some A. is not, all B is not; if all B is not, all C is not ; .: if some 

A is not, all C is not. 

4. If all A is not, all B is not ; if all B is not, some C is not ; .: if all 

A is not, some C is not. 

5. If all A is not, some B is not ; if all B is not, all C is not ; .'. if all 

A is not, all C is not. 

6. If some A is not, all B is not ; if some B is not, all C is not ; .: if 

some A is not, all C is not. 

7. If all A is not, some B is not ; if all B is not, some C is not ; .'. if all 

A is not, some G is not. 

8. If some A is not, all B is not ; if some B is not, all G is not ; .'. if some 

A is not, all G is not. 

9. If some A is not, some B is not ; if all B is not, all G is not; .'. if 

some A is not, all G is not. 

10. If all A is not, all B is not ; if some B is not, some G is not ; .: if all 

A is not, some G is not. 

11. If some A is not, some B is not; if all B is not, some G is not; .'. if 

some A is not, some G is not. 

12. If some A is not, all B is not; if some B is not, some G is not ; .'. if 

some A is not, some G is not. 



APPENDIX. 895 

IX. 

SORITES. 

See above, Vol. I., p. 385.) 
(Without order.) 

All logicians have overlooked the Sorites of Second and Third 
Figures. 

In Sorites of the Second or Third Figure, every term forms a 
syllogism with every other through the one middle term. In 
Sorites of the Fii-st Figure, every Second term at most forms a 
syllogism with every other, through its relative middle term. 

No subordination in Sorites of Second or Third Figure, ergo 
no one dominant conclusion. 

Alias In First Figure, there being a subordination of notions, 

there may be a Sorites with different middles, (all, however, in a 
common dependency). In Second and Thu'd Figures, there being- 
no subordination of terms, the only Sorites competent is that by 
repetition of the same middle. In First Figure, there is a new 
middle term for every new j)rogress of the Sorites ; in Second and 
Third, only one middle term for any number of extremes. 

In First Figure, a Syllogism only between every second term of 
the Sorites, the intermediate term constituting the middle term. 
In the others, every two propositions of the common middle term 
form a syllogism. 

Alias — There being no subordination in Second and Third 
Figures between the extremes, there, consequently, are — 

1°, No relations between extremes, except through the middle 
term. 

2°, There is only one possible middle term ; any number of others. 

3°, Every two of the terms, with the middle term, may form a 
syllogism. 

4", No order. 

Before concluding this subject, I would correct and amplify the 
doctrine in regard to the Sorites." 

1°, I would state that, by the quantification of the Predicate, (of 

« luterpciliitiun ill Zec<i«'cs. See above, Vol. I., p. 385. — Ed. 



396 APPENDIX. 

which we are hereafter to treat, in reference to reasoning in 
general), there are two kinds of Sorites ; the one descending from 
whole to part, — or ascending from part to whole ; the other pro- 
ceeding from whole to whole ; of which last it is now alone requi- 
site to speak. It is manifest, that if we can find two notions 
wholly equal to a third notion, these notions will be wholly 
equal to each other. Thus, if all trilateral figure be identical with 
all triangular figure, and all triangular figui-e with all figure the 
sum of whose internal angles is equal to two right angles, then all 
figure, the sum of whose internal angles is equal to two right 
angles, and all trilateral figure, will also be identical, reciprocating, 
or absolutely convertible. We have thus a simple syllogism of 
absolute equation. On the same principle, if A and B, B and C, 
C and D, are absolutely equivalent, so also will be A and D. We 
may thus, in like manner, it is evident, have a Sorites of absolute 
equivalence. It is not, indeed, very easy always to find four or 
more terms or notions thus simply convertible. In geometry, we 
may carry out the concrete syllogism just stated, by adding the 
three following propositions ; — All figure, the sum of whose inter- 
nal angles is equal to two rigid angles, is all figure which can he 
bisected through only one angle ; — All figure which can he hisected 
through only one angle, is all figure which, hisected through an 
angle and a side, gives two triangles ; and All figure which, thus 
hisected, gives two triangles, is all figure which, hisected through 
two sides, gives a triangle and a quadrangle, and so forth. In 
theology, perhaps, however, these series are more frequently to be 
found than in the other sciences. The following twelve equivalent 
concepts constitute at once a good example of such a Sorites, and 
at the same time exhibit a compendious view of the whole Calvin- 
istic doctrine. These are, — 1. Elected — 2. Redeemed — 3. Called — 
4. Graced with true repentance — 5. With true faith — 6. With 
true personal assurance — 7. Pardoned — 8. Justified — 9. Sancti- 
fied — 10. Endoiued with jier severance — 11. Saved — 12. Glorified. 
This series could indeed be amplified ; but I have purposely re- 
stricted it to twelve. Now, as All the elect are all the redeemed, 
all the redeemed all the called, all the called all the [truly] 
penitent, all the [tridy] penitent all the [truly'] helieving, all the 
[tr'idy] helieving all the [truly] assured, all the [truly] assured 
all the pardoned, all the ixirdoned all the justified, all the justi- 



I 
I 



APPENDIX. 



397 



Hed all the sanctified, all the sanctified all the perseverant, all 
the jjersevei'ant all the saved, all the saved all the glorified, 
all the glorified all the blest with life eternal ; it follows, of ne- 
cessity, that all the blest tuith life eternal are all the elect. To 
turn this affirmative into a negative Sorites, we have only to say, 
either at the beginning, — None of the reprobate are any of the 
elect, and, consequently, infer, at the end, that none of the blessed 
with eternal life are any of the reprobate ; or at the end, — Kone of 
the blessed with eternal life are any of the punished, and, conse- 
quently, infer that none of the punished are any of the elect. Per- 
haps the best formula for this kind of Sorites is to be found in the 
letters a, b, c. This will afford us a Sorites of six terms, viz., a, 

b, c — a, c, b — b, a, c — b, c, a — c, a, b — c, b, a — which are all vir- 
tually identical in their contents. If there be required a formula 
for a longer Sorites, we may take the letters a, b, c, d, which will 
afford us twenty- four terras. Perhaps the best formula for a de- 
scending or ascending Sorites is, for example, a, b, o, d, e, f — a, b, 

c, d, e, — a, b, c, d, — a, b, c, — a, b, — a. 

I. — COMPREHENSIVE SORITES — PROGRESSIVE AND REGRESSIVE. 



E 

Bucephalus 



A 

, Substance 




II. — EXTENSIVE SORITES. 



398 APPENDIX. 

X. 

SYLLOGISM. 

A-ITS ENOUNCEMENT— ANALYTIC AND SYNTHETIC- 
ORDER OF PREMISES. 

(See above, Vol. I., p. 395.) 

(a) ENOUNCEMENT OF SYLLOGISM. 

(Nov. 1848.) — There are two orders of enouncing the Syllogism, 
both natural, and the neglect of these, added to the not taking 
into account the Problem, or Question, has been the ground why 
the doctrine of syllogism has been attacked as involving a petitio 
yrincipii, or as a mere tautology. Thus, Buffi er cites the defi- 
nition the art of confessing in the conclusion what has been al- 
ready avowed in the premises."- This objection has never been 
put down. 

The foundation of all syllogism is the Problem. But this may 
be answered either Analytically or Synthetically. 

I. Analytically (which has been wholly overlooked) thus, — Pro- 
blem or qupesitvim, Is V Ci Answer, V is G; for V is M, and 
M is C. This in the reasoning of Depth. More explicitly : — Does 
r contain in it Cl T contains in it C ; for T contains in it M, 
and M contains in it C. But it is wholly indifferent whether we 
cast it in the reasoning of Breadth. For example : — Does C con- 
tain under tY F ? C contains under it F ; for C contains under 
it M, and M contains under it F-/3 

Here all is natural ; and there is no hitch, no transition, in the 
order of progressive statement. The whole reasoning forms an 
organic unity ; all the parts of it being present to the mind at 
once, there is no before and no after. But it is the condition of a 
verbal enouncement, that one part should precede and follow 
another. Here, accordingly, the proposition in which the reason- 

aSeconde Lor/ique, Art. iii. § 126. — thenthemmor, {that [/oodme7i so think); 

Ed. lastly the major, {that the presentiments 

y3 Plato, in a letter to Dionysius, {Epist. of divine men are of highest authority). 
2), reverses the common order of Syllo- Platonis Opera, Bekker, ix. p. 74. Cf. 
gism, placing the conclusion first, {that Melanchthon, Dialectica, L. iii., De Fig- 
he thinks there is some sense in the dead) ; uratione, p. 93, ed. 1542. 



APPENDIX. 399 

ing is absolved or realised, and which, from the ordinary mode of 
enomiceraent, has been styled the Conclusion, is stated first ; and 
the gromids or reasons on which it rests, which, from the same cir- 
cumstance, have been called the Premise ov Antecedent, are stated 
last. This order is Analytic. We proceed from the effect to the 
cause, — from the principiatum to the principia. And it is evident 
that this may be done indifferently either in Depth or Breadth ; 
the only difference being that in the counter quantities the grounds 
or premises naturally change their order. 

II. Synthetically ; — the only order contemplated by the logicians 
as natm^al, but on erroneous grounds. On the contrary, if one 
order is to be accounted natural at the expense of the other, it is 
not that which has thus been exclusively considered. For — 

1°, It is full of hitches. There is one great hitch in the separa- 
tion of the conclusion from the question ; though this latter is 
merely the former proposition in an assertive, instead of an inter- 
rogative, form. There is also at least one subordinate hitch in 
the evolution of the reasoning. 

2°, The exclusive consideration of this form has been the cause or 
the occasion of much misconception, idle disputation, and ground- 
less objection. 



(On the two Methods ; tumultuary observations, to be better 
arranged, and corrected.) 

I'', In the first or analytic order, what is principal in reality and 
in interest, is placed first, that is, the Answer or Assertion, called on 
the other order the Conclusion. 

2°, In this order all is natural ; there is no hitch, no saltus, no 
abrupt transition ; all slides smoothly from first to last. 

a) The question slides into its answer, interrogation demands 
and receives assertion. 

b) Assertion requires a reason and prepares us to expect it ; 
and this is given immediately in what, from the other order, has 
been called the Antecedent or Premises. 

c) Then the first term, either in Breadth or Depth, is taken first 
in the ground or reason, and compared with M ; then M is com- 
pared with the other. As in Breadth ; — Does C contain under it 
r ? C contains T ; for C contains under it M, and M contains 
under it V. — In Depth — Does V contain in it C? T contains in 



400 APPENDIX. 

it C ; for T contains in it M, and M contains in it C. Tliis is the 
first Figure. — Second Figure, using common language : — Is F C ? 
r is C (and C is T) ; for T and C are both the same M. Here 
the two extremes taken together are compared with M. — In the 
Third Figure M is compared with both extremes — Is F C ? V is 
C {and M is Y) ; for the same M is both V and C. 

3°, In this order there is nothing pleonastic, nothing anticipated. 

4° Nothing begged. 

- 5°, In this method the process is simple. Thought is one ; but 
to be enounced it must be analysed into a many. This order 
gives that necessary analysis, and nothing more. 

6°, In this order, when assertive, answer is limited by ques- 
tion ; good reason why, in Second and Third Figures, one answer 
should be given. 

7", This order is the one generally used by the mathematicians. 
(See Twesten, Logik, inshesondere die Analytik, § 117, p. 105, 
and below, p. 405. Plato also). 

8°, If the Qusesitum be stated as it ought to be, this order 
follows of course ; and the neglect of the qusesitum has followed 
from the prevalence of the other. If the qufesitum be stated in 
using the common form, we must almost of course interpolate a 
yes or a no before proceeding to the premises in the common 
method ; and, in that case, the conclusion is only a superfluous 
recapitulation. 

In the Synthetic, or common order, all is contrary. (The num- 
bers correspond.) 

1°, In this order, what is first in reality and interest, and in 
and for the sake of which the whole reasoning exists, comes last ; 
till the conclusion is given we know not, (at least we ought not to 
know), how the question is answered. 

2°, In this order all is unnatural and contorted by hitches and 
abrupt transitions. There is no connection between the question 
and what prepares the answer, — the premise. (Show in detail.) 

3°, In this order all is pleonastic and anticipative. The pre- 
mises stated, we already know the conclusion. This, indeed, in 
books of Logic, is virtually admitted, — the conclusion being com- 
monly expressed by a therefore, &c. Ancient doctrine of Enthy- 
meme, (Ulpian,&c.), unknown to our modern logicians; among their 



APPENDIX. 401 

other blunders on the Enthymeme. On the common doctrine, 
Logic, — Syllogistic, — is too truly defined the art of confessing in 
the conclusion what had been already avowed in the premises. 

4°, On this order the objection of petitio princijni stands 
hitherto unrefiited, if not unrefutable, against Logic * 

5°, In this order the process is complex. The simple thought 
is first mentally analysed, if it proceed, as it ought, from the quse- 
situm ; but this analysis is not expressed. Then the elements are 
recomjiosed, and this recomposition affords the synthetic an- 
nouncement of the syllogism, — the syllogism being thus the super- 
fluous regress of a foregone analysis. Aristotle's analytic is thus 
truly a synthetic ; it overtly reconstructs the elements which had 
been attained by a covert analysis.^ 

6°, In this method, the problem hanging loose from the syllo- 
gism, and, in fact, being usually neglected, it does not determine 
in the Second and Third Figures one of the two alternative con- 
clusions, which, ex facie syllogismi, are competent in them. The 
premises only being, there is no reason why one of the conclu- 
sions should be drawn to the preference of the other. Mem. 
Counter-practice old and new. The logicians ought not, however, 
to have ignored this double conclusion, 

7°, See corresponding number. 

8°, See corresponding number.7 



(h) OEDEE OF PEEMISES. 

Aristotle places the middle term in the first Figure between the 
extremes, and the major extreme first ; — in the second Figure before 
the extremes, and the major extreme next to it; — in the third 
Figure, after the extremes, and the minor extreme next to it. 

a [Stewart (JS'/e)tte>!ts, vol. ii. cb. 3, § 2, commeucing with the letters, Theinean- 

Works,Yo\. iii., p. 202, et alibi) makes ing of the term is the doctrine showing 

this objection. Refuted by GaUuppi how to analyse or reduce reasonings to 

Lez. di Locjica e di Metafisica, Lez. i, p. syllogisms ; syllogisms to figure ; figure 

2i2, et seq.'\ to mood; second and third figures to 

;8 [Aristotle's Analytics are in syn- first; syllogisms to propositions and 

thetic order ; they proceed from the terms ; propositions to terms ; for of all 

simple to the compound ; the elements these analysis is said. See Pacii Or- 

they commence with are gained by a ganon, An. Prior., i. cc. 2, 32, 42, 44, 

foregone analysis, which is not expressed. 45, pp. 128, 261, 273, 275, 278, 280.] 
They are as synthetic as a grammar 7 Compare Discussions, p. 652. — Ed. 

VOL. II. 2 



402 APPENDIX. 

In his mode of eiiouncement this rehxtive order is naturally 
kept ; for he expresses the predicate first and the subject last, 
thus : A is in all B, or A is j^i'edicated of all B, instead of 
saying AllJi is A. 

But when logicians came to enounce propositions and syllogisms 
in conformity to common language, the subject being usually first, 
they had one or other of two difficulties to encounter, and submit 
they must to either ; for they must either displace the middle term 
from its intermediate position in the first Figure, to say nothing 
of reversing its order in the second and third ; or, if they kept it 
in an intermediate position in the first Figure, (in the second and 
third the Aristotelic order could not be kept), it behoved them to 
enounce the minor premise first. 

And this alternative actually determined two opposite procedures, 
— a difference which, though generally distinguishing the logicians 
of different ages and countries into two great classes, has been 
wholly overlooked. All, it must be borne in mind, regard the 
syllogism in Figure exclusively, and as figured only in Extension. 

The former difficulty and its avoidance determined the older 
order of enouncement, that is, constrained logicians to state the 
minor premise first in the first Figure ; and, to avoid the discre- 
pancy, they of course did the same for uniformity in the second 
and third. Such is the order. 

The latter difficulty and its avoidance determined the more 
modern order of enouncement, that is, constrained logicians to 
surrender the position of the middle term as middle, in following 
the order of the major premise first in all the Figures. 

Philoponus on the First Book of the Prior Analytics, c. iv. § 4, 
(Pacian Division), f. xx. ed. Trincavelh. — " This definition ap- 
pears to be of the extremes and of the middle term ; but is not. 
It behoves, in addition, to interpolate in tliought an ' only ;' and 
thus will it be rightly enounced, as if he had said •, — But the ex- 
tremes are both that which is only in another, and that in which 
another only is. For if A is [predicated] of all B, and B is [pre- 
dicated] of all C, it is necessary that A should be predicated of all 
C. This is the first syllogistic mood. Two universal affirmatives, 
inferring an universal conclusion. For if B is in all C, conse- 
quently C is a part of B; but again B is a part of A ; consequently. 



APPENDIX. 



403 



A is in all C, inasmuch as C is a part of B. But what is here 
said will appear more clearly from a concrete example — Sub- 
stance of all animal ; animal of all man ; (there follows), sub- 
stance of all man. And backwards, [avaTrakiv), All inan ani- 
mal ; all animal substance; all 7nan therefore substance. In 
regard to this figure, it is plain how we ought to take the terms 
of the first mood. The first [major] is most generic ; the second 
[middle] is a subaltern genus ; and the third [minor] is a species 
more sjjecial than the middle. But a conclusion is here always 
necessary. Thus, following the synthetic order, that is, if we start 
from the major term, substance begins, beginning also the con- 
clusion. Substance of all animal, (substance stands first) ; animal 
of all man ; (finally the conclusion commences with substance), — 
substance of all inian. But if [on the analytic order] we depart 
from the minor term, as from man, in this case the conclusion 
will, in like manner, begin therewith: All man animal; all 
animal substance ; all man substance. " 

This is the only philosophic view of the matter. His syllogisms 
really analytic ( = in Depth.) 

Analytic and Synthetic ambiguous. Better, — order of Breadth 
and Depth."- 



a [Instances and authorities for the 
enouncement of Syllogism, with the 
Minor Premise stated first : — 

Ancients. 

Greels : — Gregory of Nyssa, Opera, t. 
ii. p. 612, in his 12 (not 10) Syllogisms 
against Manicheans, varies. These very 
coiTupt. Joannes Damascenus, Dialec- 
iica, c. 64, Opera ed. Lequien, Paris, 
1712, t. i. pp. 65, 66), gives two Syllo- 
gisms, one with minor first. Alcinous, 
De Doct. Plat. L. i. cc. 5 and 6. Aris- 
totle often places minor first. See Za- 
barella. Opera Logica, De Qicarta Fiyura, 
p. 121. Vallius, Logica, t. ii., pp. 72, 76. 
Aristotle and Alexander not regular in 
stating major propositions. See in 
First Figure, An. Pr. i. c. 4. Aristotle 
used the " whole" only of the predicate. 
See Zabarella, Tahidce, In An. Prior., p. 
149. (But see above, p. 301.) Boethius, 
Oyjera, pp. 562, 583. Aristotle, An. Pr. 



i. c. 1, suh fine, ubi Alexander, f. 9 a. 
Philoponus, f. 17 a. f . 11 b. Alexander 
Aph. In An Pr. i. ff. 9 a, 15 b. Philo- 
ponus, In An. Pr. i. ff. 11 b, 20 a. 
explains the practice of Gieek Peripa- 
tetics in this matter. See also ff 17 a, 
18 a; and 11 a, 21 a — these in i. Fig. — 
in ii. Fig. 23 b. The same In Phy.sica, 
i. c. 1, f. 2. Themistius, In An. Post. 
ii. c. 4. Anonymiis, De Syllogismo, f. 
43 a. Gregorius Aneponymus, Com- 
pend. Philosophi(e Syntagma. L. v. cc. 
1, 6, pp. 58, 70. Georgius Diaconus 
Pachymerius, Epit.Log. tit. iv. cc. 1 — 4. 
Sextus Empiricus, Pyn'h. Hypotypos., 
L. ii. cc. 13, 14, pp. 103, 110. Clemens 
Alex. Stroyn. L. viii. Opera, p. 784, (ed. 
Sylburgii.) Blemmidas, Epitome Logica, 
c. 31, p. 219. Gregorius Trapezun- 
tius, Dialectica, De Syll. p. 30. " Prima 
(Figura) est in qua medius terminus 
subjicitur in majore, et in minore 
prfcdicatur: quamvis contra fieri et soleat 



404 



AITENDTX, 



R FIGURE— rXFIGUKED AXP FIGURED SYLLOGISM. 
(1S5S) (a) Contrast axd Compakijon or tue taeious 

KI>vDS OP FOK^LAi SYLLOOI^M — DrFFEKEXCE OF 
FlOrRE AOCIDE^~TAL. 

A). Unjjgured SifUogi.sm — One form of syllogism : for here there 
is abdislied, 1^, The difference of Breadth and Depth, for the t^rms 



rf pnmtS" A Greek, he -wrote in Italv 
for tike Latins; but refers here to the 
practioe of his conntrrmen. 

Latism : — CSeero, 2>f Finu ia. 8 ; iv. IS. 
TWc, J)M!?T-iii. 7 ; T. 15, Opera Phil, pp. 
SS5, S>OS, dSl, 1029, edTerbtn^ Mac- 
rolmis, Opera-, p. ISl, ZeuniL Seneca, 
E^-nst S5, p S6S. Apuleius, 3c MahiL 
jDoct Plat Li. iii. p. S5, ed. Elmenhorst. 
Isidciirus, in GotJiqfr. Aurt<>rcs, p. S7S. 
Casaodorus, jyiahciica, Oftovi.^ p. 556, 
Grenev. 1650, gires altrOTiaiiTe, but in 
Psalm •yvri.T. 16, gi"res a svDogisin ■wTth 
minor first. Mardanxis Capella, Ik Sfp- 
tem Artihug Zibcralibn-R, aHows both 
forms for first Figure ; geaierallT makes 
the minor first (see below, p. -424), Boe- 
thius, (origo maliV t. 0}'i€ra, p. 5^ d 

OSIEKIALS. 

IS ' - : — ^Axerrc^es (enouncing 

as TTr _ . : __ t Jigares, has minor firsx. 
(See below, p. 425. 1 

JetD^: — Eabbi Simeon [tnilT Maimon- 
id«] (in Hebrew.) Loffiaa, per S. Mnn- 
stem TD ec. 6, 7, Basil, 1527- 

Modem antieipatioiis of iie doctrine 
ihai the Minor Premisse shoxild precede 
the Major. YaHa, DiaJ^ectica, i. 60 b, &.c. 
Opera p. 7§3, 7S6. Joanna Xeomagus, 
In TrapezuniiuTn, i S8 b. (only adduce 
examples.) Caramuel, Bat. et Mealu Phi- 
loBopMa, Loaica. Disp. ix. XTi Aquinas, 
OpiiiT. 47. ^Camerarius. Difp. Phil, P. L 
qu. IS, p. 117. > Alstedius, EihOfclopa- 
rfwjp. 4i7. Ga^endi, Oj>era, iL p. 413 ; 
L p. 107. Cameraiins, Disp. PML P. L 
qu. IS, p. 117. Leibnita, Opera ix Pais. 



i. p. S56. iKsscrf. de Arte Comhimahtria, 
(1666^, ed Dutens, who refeis to Ramus, 
Gassendi, Alcinous, &c Cf. ^Tonrcayjr 
Essais, L ir, § S, p. 454, ed. Raspe : and 
Locke's Egnay, ibid. Buffier. Zx^i-ptf, 
§ 6S. Csisaiius, Dijil^ti^a. Tract, t. Ik 
S^IL Cat p. 15S, vfiis^ e^- 15-5-^- J- C.E. 
Xoira iMt'CcM Vcrita-f. kc, see Reusoh, 
5 7 ; " " '26. Chau- 

v: , r. Figvra. 

Hobt'es, L-.'.^ -'J.',,, 0, IT. prefix^ the 
minor, I'see HaBam, Lit of Enropf^ vol. 
iii c- f ■ ed. lS-3?.^ - 

Xcucs "- 36, § 225. 1 



Lopl; § 



pp. 202, 223. ii^.1 



$ 454. Esser, Lo^tJr, § 107, p- 
•;: ■: _ ; 5 114, p 40S. Beneke, 

.> J .. c T. p. 210 (i iteq. 

Stapuiensis, in Sergeant's J/fMod to 
S'iencf, p, 127. F:i::::'lati, vthough he 
eiTS himseh' } i Lc-pi'dT, p. S65 

P. iil c. S, :: - : ^ ^ -_ r re Boethius, Sex- 
T 115 Emj'iricTiSs Aieinous, &c, Ch. Mayne 
is-sjz 0% ^S'atiiraJ A'i'»riti»^, p 122 ff «■?. 
Lamy, Acta Eru'^„ 170S, p. 67. 

"VTho haxe erred in this subject. — 
making our ordo- of enuiMsataon the 
natural and ii": n" VVes, Cemfvra Vert. 
Opera, %. i. " . G. Tossius. Be 

yai. Art. 1,-. u... L.,i^yi, c viiL § 9. 
J. A. Fabridus, Ad. Sext. Em p. 103. 



Faeciolati, iT ' " 
Waitz, Ir, (■ 

That Rf.- - 

Qtantrty n. - " 
Mai^ § 3?&, p. c.:. :. 
Logicum, § 5i7. Schul;. 
old, aS17) § 72 of last 



■ - 7. S6. 

. :_: rr_cnsiTe 

Wolf, PJiil. 

,1. ^ . !^ema 

. ; 77 of 

^i•-; edition. 



ars ^I'tJ: ^~'*"'^' 



AFPES338K. 



4m 



-iSfi irx!-- 



-X levTi- 



""fflasiasi 






tjSI iSir Jffli^IH3Ci& 






im nf ■?.(/7.it iirrici, jgrTiHrr^ smn— Zrcinini 



jf im iLioiJE'i if HJiuiujnc.. 1.. Ijit.. Zx j?araF- 

TaoLsi. -ZaS: WmTr- Zl^l+IIIIHfc. llff ^ ;= Sb 
SSiCTr SS^St 'al& '""ftrnTfriwHrnT icSE. {Iff JL = 

H. jrar A = M. 'aw£ JE = JS .. nr iai.^ :ffis 



406 APPENDIX. 



If rule true, it will follow that it is of no consequence whether : — 
]°, The middle one or any other of the three terms be, in any 
proposition, subject or predicate, if only either. Hence difference 
of Figure of no account in varying the syllogism. Thus, (retain- 
ing the subordination of terms), convert major proposition in Ex- 
tension of first Figure, and you have second Figure ; convert 
minor proposition, and you have third Figure ; convert both pre- 
mises, and you have fourth Figure. 

2°, Whether one of the extremes, one or other of the premises, 
stand first or second, be, in fact, major or minor term of a propo- 
sition ; all that is required is, that the terms and their quantities 
should remain the same, and that they should always bear to each 
other a relation of subject and predicate. Thus, if [in] any of the 
Figures, the major and minor terms and projiositions interchange 
relation of subordination ; when, in the first Figure, you convert 
and transpose ; and when [in] the other three Figures (fourth ?), 
you simply transpose the premises. 

Indifferent (in first Figure) which premise precedes or follows. 
For of two one not before the other in nature. But not indiffer- 
ent in either whole, which term should be subject and predicate 
of conclusion.* 

(b) Double Conclusion in Second and Thied Figures. 

My doctrine is as follows : — 

In the Unfigured Syllogisin there is no contrast of terms, the 
notions comjiared not being to each other subject and predicate ; 
consequently, the conclusion is here necessarily one and only one. 

In the Figured Syllogisin we must discriminate the Figures. 

In the First Figure, where the middle term is subject of the one 
extreme and predicate of the other, there is of course a determinate 
major extreme and premise, and a determinate minor extreme and 
premise ; consequently, also, one proximate or direct, and one remote 
or indirect, conclusion, — the latter by a conversion of the former. 

« Compare Discussions, p. 6o3. — Ed. 



APPENDIX. 407 

In the Second and Third figures all this is reversed. In these 
there is no major and minor extreme and premise, both extremes 
being either subjects or predicates of the middle ; consequently, 
in the inference, as either extreme may be indifferently subject or 
predicate of the other, there are two indifferent conclusions, that 
is, conclusions neither of which is more direct or indirect than the 
other. 

This doctrine is opposed to that of Aristotle and the logicians, 
who recognise in the Second and Third Figures a major and minor 
extreme and premise, with one determinate conclusion. 

The whole question in regard to the duplicity or simplicity of 
the conclusion in the latter figures depends upon the distinction 
in them of a major and a minor term ; and it must be peremp- 
torily decided in opposition to the universal doctrine, unless it can 
be shown that, in these figures, this distinction actually subsists. 
This was felt by the logicians ; accordingly they applied themselves 
with zeal to establish this distinction. But it would apjDcar, from 
tlie very multiplicity of their opinions, that none jiroved satisfac- 
tory ; and this general presumption is shown to be correct by the 
examination of these opinions in detail, — an examination which 
evinces that of these opinions there is no one which ought to 
satisfy an inquiring mind. 

In all, there are six or five different grounds on wdiich it has 
been attempted to establish the discrimination of a major and 
minor term in the Second and Third Figures. All are mutually 
subversive ; each is incompetent. Each following the first is in 
fact a virtual acknowledgment that the reason on which Aristotle 
proceeded in this establishment, is at once ambiguous and insuffi- 
cient. I shall enumerate these opinions as nearly as possible in 
chronological order. 

1. That the major is the extreme which lies in the Second 
Figure nearer to, in the Third Figure farther from., the middle. — 
This is Aristotle's definition, {An. Pr., L. i., cc. 5, 6). At best it 
is ambiguous, and has, accordingly, been taken in different senses 
by following logicians ; and in treating of them it will be seen 
that in none, except an arbitrary sense, can the one extreme, in 
these figures, be considered to lie nearer to the middle term than 
the other. I exclude the supposition that Aristotle spoke in 
reference to some scheme of mechanical notation. 



408 APPENDIX. 

2. That the major term in the antecedent is that ivhich is pre- 
dicate ill the conclusion. — This doctrine dates from a remote an- 
tiquity. It is rejected by Alexander; bnt, adopted by Ammonius 
and Philoponus, (f. 17 b, 18 a., ed. Trine), has been generally 
recognised by subsequent logicians. Its recognition is now almost 
universal. Yet, critically considered, it explains nothing. Educing 
the law out of the fact, and not deducing the fact from the law, it 
does not even attempt to show why one being, either extreme may 
not be, predicate of the conclusion. It is merely an empirical, — 
merely an arbitrary, assertion. The Aphrodisian, after refuting 
the doctrine, when the terms are indefinite (preindesignate), justly 
says : — " Nor is the case different when the terms are definite 
[predesignate]. For the conclusion shows as predicate the term 
given as major in the premises ; so that the conclusion is not itself 
demonstrative of the major ; on the contrary, the being taken in 
the premises as major, is the cause why a term is also taken as 
l^redicate in the conclusion." — [An. Pr. £ 24 a, ed. Aid.) 

3. That the proximity of an extreme to the middle term, in 
Logic, is to be decided hy the relative p)roxiniity in nature, to the 
7niddle notion of the notions compared. This, which is the inter- 
pretation of Aristotle by Herminus, is one of the oldest upon re- 
cord, being detailed and refuted at great length by the Aphrodi- 
sian, (f 23 b, 2-i a). To determine the natural proximity re- 
quired is often difficult in affirmative, and always impossible in 
negative, syllogism ; and, besides the objections of Alexander, it is 
wholly material and extralogical. It is needless to dwell on this 
opinion, which, obscure in itself, seems altogether unknown to our 
modern logicians. 

4. That the major term in the Syllogism is the p)redicate of 
the problem or question. This is the doctrine maintained by 
Alexander, (f 24 b) ; but it is doubtful whether at first or second 
hand. It has been adopted l^y Averroes. Zabarella, and sundry of 
the acuter logicians in modern times. It is incompetent, however, 
to establish the discrimination. Material, it presupposes an inten- 
tion of the reasoner ; does not appear e^/ac?'e syllogismi; and, at 
best, only shows Avhich of two possible qu^esita, — which of two 
possible conclusions, — has been actually carried out. For it as- 
sumes, that of the two extremes either might have been major in 
the antecedent, and predicate in the conclusion. If Alexander 



APPENDIX. 409 

had applied the same subtlety in canvassing his own opinion, 
which he did in criticising those of others, he would not have 
given the authority of his name to so untenable doctrine. 

5. That the major extreme is that contained in the major jwe- 
mise, and the major premise that in the order of enouncement 
first. This doctrine seems indicated by Scotus, (An. Pr., L. i., 
qu. xxiv. §§ 5, 6) ; and is held explicitly by certain of his fol- 
lowers. This also is wholly incompetent. For the order of 
the premises, as the subtle Doctor himself observes, {Ih., qu. 
xxiii. § 6), is altogether indifferent to the validity of the con- 
sequence ; and if this external accident be admitted, we should 
have Greek majors and minors turned, presto, into Latin minors 
and majors. 

6. That the major extreme is that contained in the major pre- 
mise, and the major premise that itself most general. All oppo- 
site practice originates in abuse. This opinion, which coincides 
with that of Herminus, (No. 3), in making the logical relation of 
terms dependent on the natural relation of notions, I find ad- 
vanced in 1614, in the Disjmtationes of an ingenious and inde- 
pendent philosopher, the Spanish Jesuit, Petrus Hurtado de Men- 
doza, {Disp.Log. et Met., I., Disp. x. §§ 50 — 55). It is, however, 
too singular, and manifestly too untenable, to require refutation. 
As material, it is illogical ; as formal, if allowed, it would at best 
serve only for the discrimination of certain moods ; but it cannot 
be allowed, for it would only subvert the old without being ade- 
quate to the establishment of aught new. It shows, however, how 
unsatisfactory were the previous theories, when such a doctrine 
could be proposed by so acute a reasoner, in substitution. This 
opinion has remained unnoticed by posterior logicians. 

The dominant result from this historical enumeration is, that, 
in the Second and Third Figures, there is no major or minor term, 
therefore no major or minor premise, therefore two indifferent 
conclusions. 

This important truth, however natural and even manifest it may 
seem when fully developed, has but few and obscure vaticinations 
of its recognition during the progress of the science. Three only 
have I met with. 

The first I find in the Aphrodisian, (f 24 b) ; for his expres- 
sions might seem to indicate that the opinion of there being no 



410 APPENDIX. 

major and minor term in the second figure, (nor, by analogy, in the 
third), was a doctrine actually held by some early Greek logicians. 
It would be curious to know if these were the " ancients," assailed 
by Ammonius, for maintaining an overt quantification of the pre- 
dicate. The words of Alexander are : — " Nor, however, can it be 
said, that in the present figure there is no major. For this at least 
is determinate, — that its major must be universal ; and, if there be 
in it any syllogistic combination, that premise is the major, which 
contains the major term ; " (f 24 a.) Demurring to this refuta- 
tion, it is, however, evidence sufficient of the opinion to which it 
is opposed. This, as it is the oldest, is, indeed, the only authority 
for any deliberate doctrine on the point. 

The second indication dates from the middle of the fifteenth 
century, and is contained in the Dialectica of the celebrated Lau- 
rentius Valla (L. iiL c. 8 [51]). Valla abolishes the third figure, and 
his opinion on the question is limited to his observations on the 
second. In treating of Cesare and Camestres, which, after a host 
of previous logicians, he considers to be a single mood ; there is 
nothing remarkable in his statement : " Neque distinctre sunt pro- 
positio et assumptio, ut altera major sit, altera minor, sed quodam- 
modo pares ; ideoque sicut neutra vindicat sibi primum aut secun- 
dum locum, ita utraque jus habet in utraque conclusione. Verum 
istis placuit, ut id quod secundo loco poneretur, vendicaret sibi con- 
clusionem : quod verum esset nisi semper gemina esset conclusio. 
Sed earum dicamus alteram ad id quod primo loco, alteram ad id 
quod secundo loco positum est referri" We, therefore, await the 
development of his doctrine by relation to the other moods, Festino 
and Baroco, which thus auspiciously begins : — " Idem contingit in 
reliquis duobus : qui tamen sunt magis distincti." We are, how- 
ever, condemned to disappointment. For, by a common error, 
excusable enough in this impetuous writer, he has confounded sin- 
gulars (definites) with particulars (indefinites) ; and thus the ex- 
amples which he adduces of these moods are, in fact, only examples 
of Cesare and Camestres. The same error had also been previ- 
ously committed (L. iii. c. 4.) The whole, therefore, of Valla's 
doctrine, which is exclusively founded on these examples, must go 
for nothing ; for we cannot presume, on such a ground, that he 
admits more than the four common moods, identifying, indeed, the 
two first, by admitting in them of a double conclusion. We can- 



APPENDIX, 411 

not, certainly, infer, that he ever thought of recognising a par- 
ticular, — an indefinite, predicate in a negative proposition. 

The third and last indication which I can adduce is that from 
the Method to Science of John Sergeant, who has, in this, as 
in his other books, (too successfully), concealed his name under 
the initials " J. S." He was a Catholic priest, and, from 1665, an 
active religious controversialist : whilst, as a philosopher, in his 
Idea Philosophice Gartesianw, a criticism of Descartes, in his 
Solid Pliilosophy, a criticism of Locke," in his Metaphysics, and in 
the present work, he manifests remarkable eloquence, ingenuity, 
and independence, mingled, no doubt, with many untenable, not to 
say ridiculous, jiaradoxes. His works, however, contain genius 
more than enough to have saved them, in any other country, from 
the total oblivion into which they have fallen in this, — where, in- 
deed, they probably never were appreciated. His Method to Sci- 
ence, (a treatise on Logic), was published in 1696, with a "Preface, 
dedicatory to the learned students of both our Universities," ex- 
tending to sixty-two pages. But, alas ! neither this nor any other 
of his philosophical books is to be found in the Bodleian. 

In the third book of his Method, which treats of Discourse, 
after speaking of the first, or, as he calls it, " only right figure of a 
syllogism," Ave have the following observations on the second and 
third : — " § 1 4. Wherefore the other two figures, [he does not recog- 
nise the fourth], are imnatural and monstrous. For, since nature 
has shown us, that what conjoins two notions ought to be placed 
in the middle between them ; it is against nature and reason to 
place it either above them both, as is done in that they call the 
second figure, or under them both, as is done in that figure they 
call the third. 

" § 15. Hence no determinate conclusion can follow, in either of 
the last figures, from the disposal of the parts in the syllogisms. 
For since, as appears, (§ 13), the extreme which is predicated of 
the middle term in the major, has thence a title to be the predi- 
cate in the conclusion, because it is above the middle term, which 
is the predicate, or above the other extreme in the minor, it fol- 

« Sergeant is an intelligent antagonist certain views he anticipates Kant ; and 

of both these philosophers, and I have Pope has evidently taken from his bro- 

else where had occasion to quote hina as ther Catholic the hint of some of his 

the first and one of the ablest critics of most celebrated thoughts. 
the Essay on Human Understanding. In 



412 APPENDIX. 

lows, that if the middle term be twice above or twice heloiu the 
other two terms in the premises, that reason ceases ; and so it is 
left indifferent which of the other terms is to be subject or predi- 
cate in the conclusion ; and the indeterminate conclusion follows, 
not from the artificial yb?"m of the syllogism, but merely from the 
material identity of all the three terms ; or from this, that their 
notions are found in the same Ens. Wherefore, from these pre- 
mises, [in the second figure], 

Some laudable thing is [all] virtue, 
[All] courtesi/ is a virtue ; 

or, from these, [in the third], 

[All] virtue is [somel laudable, 
Some virtue is [all] courtesy ; 

the conclusion might either be, 

Therefore, [all] courtesy is [some] laudable. 
Or, So7ne laudable thing is [all] courtesi/. 

So that, to argue on that fashion, or to make use of tliese awk- 
ward figures, is not to know certainly the end or conclusion we 
aim at, but to shoot our bolt at no determinate mark, since no 
determinate conclusion can in that case follow." (P. 232). 

Extremes, it is said, meet. Sergeant would abolish the second 
and third figures, as petitory and unnatural, as merely material 
corruptions of the one formal first. I, on the contrary, regard all 
the figures as equally necessary, natural, and formal. But we 
agree in this : both hold that, in the second and third figures, there 
is a twofold and indifferent conclusion ; howbeit, the one makes 
this a monstrosity of the syllogistic matter, the other, a beauty of 
the syllogistic form. Therefore, though I view Sergeant as wrong 
in his premises, and " shooting his bolt at no determinate mark," 
I must needs allow that he has, by chance, hit the bull's eye. I 
have inserted, within square brackets, the quantifications required 
to restore and show out the formality of his examples ; on my 
scheme of notation, they stand as follows : — 



r 





APPENDIX. 413 



C— HISTORICAL NOTICES REGARDING FIGURE OF 
SYLLOGISM. 



I. — Aristotle. 

Aristotle ; Figures and Terms of Syllogism, Prior Analytics 
B. I. ch. iv. 

First Figure, ch. iv. — § 2. " When three terms [or notions] hold 
this mutual relation, — that the last is in the whole middle, whilst 
the middle is or is not in the whole first, — of these extremes 
there results of necessity a perfect syllogism.* 

§ 8. " By middle term, [B (B)], I mean that which itself is in 
another and another in it ; and which in position also stands in- 
termediate. I call extreme both that which is itself in another 
[the minor], and that in which another is [the major]. For if A 
be predicated of all B, and B of all C, A will necessarily be pre- 
dicated of all C. 

§ 10. "I call that the major extreme [A (A)] in which the 
middle is; the minor [r (C)] that which lies under the middle." 

Second Figure, ch. v. — § 1. " When the same [predicate notion] 
inheres in all of the one and in none of the other, or in all or in 
none of both [the subject notions], — this I denominate the Second 
Figure. 

§ 2. " The 7niddle [M (M)] in this figure I call that which is 
predicated of both [notions] ; the extremes, the [notions] of which 
the middle is said. The major extreme [N (N)] is that towards 

a Ch. iv. § 2. — This definition of the the higher notion A : and with reference 
First Figure, (founded on the rules De to comprehension, — for the higher no- 
Omni and de Nullo), ai:)plies only to the tiou A as contained in the all or whole 
universal moods, but, of these, onlj' to of the lower notion B. In the former 
those legitimate and useful, — Barbara sense, which with Ai-istotle is the more 
and Celarent. It, therefore, seems in- usual, and, in fact, the only one con- 
adequate, but not superfluous. templated by the logicians, there is also 

Aristotle uses the phrase " to be in to be observed a distinction between 

all or in the wJiole," both with reference the inhesion and the predication of the 

to extension, — for the lower notion B, attribute, 
as contained under the all or whole of 



414 



APPENDIX. 



the middle ; the minor [3 (0)], that from the middle more 
remote. 

§ 3. " The middle is placed out [from between] the extremes, 
the first in position" — 



[So, M 

N 



M 

■N 




Third Figm-e, eh. vi. — § 1. "Wlien in the same [subject notion] 
one [predicate notion] inheres in all, another in none of it, or 
when both inhere in all or in none of it, such figure I call the 
Third. 

§ 2. " In this [figure] I name the middle, that of which both 
[the other terms] are predicated ; the extremes, the predicates 
themselves. The major extreme [n (P)] is that farther from, the 
minor [P, (Q)], that nearer to, the middle. 

§ 3. " The middle [^ (R)] is placed out [from between] the 
extremes, the last in position," 



[As, n 
p 

2 



Aristotle, Prior Ancdytics, B. i. c. 23, § 7. 

General Theory of Figure. — " If, then, it be necessary [in reason- 
ing] to take some [term] common [or intermediate] to both [ex- 
treme terms] ; this is possible in three ways. For we predicate 
either [the extreme] A of [the middle] C, and [the middle] C of 
[the extreme] B ; or [the middle] C of both [extremes] ; or both 
[extremes] of [the middle] 0. These are the [three] Figures of 
which we have spoken ; and it is manifest, that through one or 
other of the Figures every syllogism must be realised."" 



a Aristotle here varies the notation tion might appear to indicate), that the 

liy lettex's of the three syllogistic terms middle term was a notion in the First 

making C (r) stand for the middle Figure, necessarily intermediate be- 

term, A and B for the two extremes, tween the two extremes, in the Se- 

This he did, perhaps, to prevent it be- cond superior, in the Third inferior, to 

ing supposed, (what his previous nota- them. 



APPEIfDIX. 415 

II. AND III. — AlEXANDEE AND HeEMINUS. 

Alexander, In An. Pr.^ f. 23 b. 

Second Figure, c. v. Aristotle. — " ' The middle extreme is that 
which lies towards the middle.' 

§ 2. " But it is a question, whether in the Second Figure there 
be by nature any major and minor extreme, and if there be, by 
\vhat criterion it may be known. For if we can indifferently con- 
nect with the middle term whichsoever extreme we choose, this 
we may always call the major. And as negative conclusions only 
are drawn in this figure, universal negatives being also mutu- 
ally convertible, it follows, that in universal negatives the one 
term has no better title to be styled major than the other, seeing 
that the major term is what is predicated, whilst both are here 
indifferently predicable of each other. In universal affirmatives, 
indeed, the predicate is major, because it has a wider extent ; and 
for this reason, such propositions are not [simply] convertible ; 
so that here there is by nature a major term which is not to be 
found in universal negatives. 

" Herminus is of opinion that, in the Second Figure, 

[1°.] "If both the extremes, of which the middle is predicated, 
be homogeneous [or of the same genus], the major term is that most 
proximate to the genus common to the two. For example : — 
If the extremes be bird and man ; hird lying nearer to the com- 
mon genus [cinimal] than man, as in its first division, hird is 
thus the major extreme ; and, in general, of homogeneous terms, 
that holding such a relation to the common genus is the major. 

[2°.] "But if the terms be equally distant from the common genus, 
as horse and man, we ought to regard the middle predicated of 
of them, and consider of which [term] it is predicated through 
[that term] itself, and of which through some other predicate ; 
and compare that through which it is predicated of another with 
that through which it is predicated of [the term] itself. And if 
that through which [the middle] is predicated of another, (viz. 
the one extreme), be nearer [than the other extreme] to the 
common genus, that [extreme] of which [for rovTOiv ov, I read 
TovTov ov\ the middle is [mediately] predicated, from its closer 
propinquity to the common genus, rightly obtains the title of 
major. For example : If the extremes be horse and man, 



416 ArPENDIX. 

rational being predicated of them, — negatively of horse, affirma- 
tively of man ; seeing that rational is not of itself denied of 
horse, but because horse is irrational, whereas 7'ational is of 
itself affirmed of man, horse is nearer than man to their common 
genus animal ; horse will, therefore, be the major extreme, though 
man be no further removed than horse from its proper genus. 
And this, because that through which the predicate [i.e. the middle] 
is predicated of this last, as being irrational, is greater ; for ra- 
tional is not denied of horse qua horse, whilst it is affirmed of 
onan qua man. 

[3°.] " But if the extremes be not homogeneous, but under ditfe- 
rent genera, that is to be considered the major term, which of the 
two holds the nearer of its own genus. For instance : If aught be 
predicated of colour and man, colour is the major extreme ; for 
colour stands closer to q ual it i/, tlmn man to substance: as man 
is an individual [or most special] species, but not colour. 

[4°.] "Finally, if each be equally remote from its proper genus, 
we must consider the middle, and inquire of which term it is pre- 
dicated through [that term] itself, and of which through some- 
thing else ; and if that, through which the middle is predicated 
of another, [i.e. one extreme], be nearer to its proper genus, and if 
through that the middle be actually predicated of this term, this 
term is to be deemed the major. For example : If the terms be 
white and man, the one being an individual species in quality, the 
other in substance ; and if rational be affirmatively predicated of 
man, negatively of white ; the affirmation is made in regard 
to man as mcin, whereas the negation is made of white, not as 
wJiite, but as inanimate. But since inanimate, through which 
rational is denied of white, is more common, more universal, and 
more proximate to substance inanimate than man to [suhstance'\ 
animate, on that account, white is the major term in preference to 
man!' [So far Herminus.] 

" But to reason thus, and to endeavour to demonstrate a major 
term by nature, in the Second Figure, is a speculation which may 
be curious, but is not true. [I read Trpog tw.] 

[1°]. " For, in the first place, if we consider the given terms, 
not in themselves, but in relation to others, in which the predi- 
cated term does not inhere ; the major term will be always found 
in the negative proposition. For, in this case, the major is always 



APPENDIX. 417 

equal to the middle terra ; since whether it be thus or thus taken 
from the commencement, or be so made by him who denies it, the 
negative major will still stand in this relation to the middle term. 
For the middle does not inhere, where it is not suj)posed to inhere. 
Wherefore, its repugnant opposite inheres in the subject, but the 
repugnant opposite of the middle is equal to the middle. And 
this, either through the middle itself, or through another notion of 
wider extent ; as when rational is denied of something through 
inanimate. For there is here an equalisation through irrational, 
through which rational is negatively predicated of horse. For 
either the middle is equal to this of which it is denied, or [I read, 
Ty for 6] it is less ; as when, through inanimate, rational is de- 
nied of aught. For inanimate is equal to animate, under which 
is rational, a notion greater than that other of which it is affirmed. 
For since the affirmative predicate is greater than its subject, of 
which the middle is denied or not affirmed ; and since the reason 
why the middle is denied, is equal to or greater than the middle 
itself, which middle, again, in an affirmative proposition, is greater 
than its subject ; — on these accounts, a negative proposition is 
always greater than an affirmative. Nevertheless, Aristotle him- 
self says that a negation is to be placed in the minor [proposi- 
tion] ; for the second syllogism in this figure [Camestres] has as 
its minor premise an universal negative. 

[2°]. " Further, why in the case of negatives alone should explan- 
ation or inquiry be competent, in regard to the reason of the nega- 
tive predication, seeing that in the case of affirmatives the reason 
is equally an object of inquiry? For rational is predicated of 
man, of itself, indeed, but not primarily, that is, not inasmuch as 
he is man, but inasmuch as he is rational; so that if rational 
[be denied] of Jiorse through iri^ational, still these are both 
branches of the same division. By this method, assuredly, no 
major can be ever found. Wherefore, we ought not, in this way, 
to attempt a discrimination of the major of affirmative syllogisms 
in the Second Figure. For in this figure affirmation and negation 
are equally compatible with the major term ; so that whatsoever 
term has by the forementioned method been found major, the same, 
taken either as major or minor, will efiectuate a syllogistic juga- 
tion ; which being competent, there is no longer any major [or 
minor] in this figure. For the problem is to find not a major 

VOL. II. 2 D 



418 APPENDIX. 

term absolutely, but one of this figure." [So much touching Her- 
minus.] 

[3°]. " Nor, on the other hand, as is thought by some, is that un- 
conditionally to be called the major term, which stands predicate 
in the conclusion. For neither is this manifest ; if left indefinite 
[preindesignate], the same term will hold a different relation, 
thouo;li a conversion of the universal neo;ative ; so that what is 
now the major, may be anon the minor ; we may, in fact, be said to 
constitute the same term both major and minor. Naturally there 
is in negative propositions no major notion, nor, from the conclu- 
sion, ought we to make out the major at all. Nor is the case 
different when the term is defined [predesignate]. For the con- 
clusion shows, as predicate, the term given as major in the pre- 
mises ; so that the conclusion is not itself demonstrative of the 
major ; on the contrary, the being taken in the premises as 
major is the cause why a term is also taken as predicate in the 
conclusion. 

" Nor, however, can it be said that in this figure there is no major. 
For this at least is determinate, — that its major must be universal; 
and, if there be [in it] any syllogistic combination, that premise is 
the major which contains the major term. 

[4°] " But, in the Second Figure, which of the terms is to be 
deemed the major ? That is to be deemed the major, and to be 
placed first, which in the problem [question or quresitum] we intend 
to demonstrate, and which we regard as predicate. For every one 
who reasons, first of all determines with himself, what it is he 
would prove ; and to this end he applies his stock of suitable pro- 
positions ; for no one stumbles by chance on a conclusion. The 
notion, therefore, proposed as predicate in the problem to be 
proved, is to be constituted the major term ; for although the pro- 
position be converted, and the notion thereby become the subject, 
still in what we proposed to prove, it [actually] was, and, there- 
fore, [virtually] remains, the predicate. Hence, even if there be 
drawn another conclusion, w^e convert it ; so that, to us who prove 
and syllogise and order terms, that always stands as the major. 
For major and minor are not, in negative syllogisms, regulated by 
their own nature, but by the intention [of the reasoner] to con- 
clude. Thus it is manifest, that what is the predicate in the pro- 
blem, is also the predicate in the conclusion." 



APPENDIX. 419 

Alexander on Prior Analytics, L. i. c. vi., f. 30 a. ed. Aid. 

(Third Figure.) . . . This is the Third Figure, and holds the 
last place because nothing universal is inferred in it, and because 
sophistical syllogisms chiefly aff'ect this figure with their indefinite 
and particular conclusions. But the sophistical are the last of all 
syllogisms. . . . Add to this, that while both the Second and 
Third Fio;ures take their origin from the First of the two, the 
third is engendered of the inferior premise. For the minor, qua 
minor, is the inferior premise, and holds reasonably a secondary 
place, [the conversion of the minor proposition of the first figure 
giving the third figure]. 

F. 30 b. (Darapti.) " The first syzygy in this figure is of two 
universal affirmatives [Darapti.] But it may be asked — Why, 
whilst in the second figure there are two syllogistic conjugations, 
having one of the premises an universal affirmative, the other an 
universal negative, (from having, now their major, now their 
minor, as an universal negative proposition converted) ; — why, in 
the third figure, there is not, in like manner, two syllogistic com- 
binations of two universal affirmatives, since of these, either the 
major or the minor proposition is convertible ? Is it that in the 
second figure, from the propositions being of diverse form [quality], 
the commutation of a universal negative into something else by 
conversion is necessary, this being now the major, now the minor, 
and it not being in our power to convert which we will ? In the 
third figure, on the other hand, there being two universal affirma- 
tives, the position [relation] of the propositions, (for they are simi- 
lar in character and position), is not the cause of one being now 
converted, now another ; the cause lying in us, not in the jugation. 
Wherefore, the one or other being similarly convertible, inasmuch 
as the position [relation] of the two propositions is the same ; the 
one which aff'ords the more important probation is selected, and 
hereby is determined the syllogistic jugation. Moreover, tlie dif- 
ferences of syllogism [moods] in each figure are eff'ected by the 
diff'erences among their jugations, not by those among their proba- 
tions. Thus that the combination of propositions is syllogistic [or 
valid], is proved by conversion and reductio ad imjwssibile, also by 
exposition. But from this circumstance there does not emerge a 
plurality of syllogisms [moods]. For the different probations [are 
not valid from such plurality, but] from the unity of the jugation 



.4 



420 APPENDIX. 

from which they are inferred, so that one j ligation of two universal 
affirmatives may constitute, in the third figure, a single syllogism 
[mood], howbeit the probations are different ; inasmuch as now 
the one, now the other, of the propositions can be converted." 

IV. — Philoponus. 

Philoponus (or rather Ammonius) on Aristotle, An. Pr., i. 4, 
§ i. f 17 a. ed. Trincavelli, 1536. 

" The Predicate is always better than the Subject, because the 
predicate is, for the most part, more extensive (cTrt irXeov) than the 
subject, and because the subject is analogous to the matter, the 
predicate to the form ; for the matter is the subject of the forms. 
But when the middle term is predicated of the two extremes, or is 
the subject of both ; in this case, it is not properly intermediate. 
But, howbeit, though in position external to the middle, it is still 
preferable to be the predicate than to be the subject. On this 
ground, that is called the first figure, the middle term of which 
preserves its legitimate order, being subject of the one extreme, 
and predicate of the other. The second figure is that in which the 
middle is predicated of both extremes, and in which it occupies 
the better position of those remaining. Finally, the third figure 
is that in which the middle term is subjected to the two extremes ; 
here obtaining only the lowest position. Wherefore, in the first 
figure the middle term is delineated on a level with the extremes ; 
whereas in the second it is jjlaced above, and in the thkd below, 
them."« 

Philoponus (or rather Ammonius) on Aristotle, An. Pr., f 17 
a, ed. Trincavelli, 15.36. 

a Ammonius, or Philoponus, here ma- than Ammonius does not appear ; for 
nifestly refers to the diagrams represent- they are probably not the constructions 
lug the three figures, and accommodated referred to by Aristotle ; and none are 
to Aristotle's three sets of letters, noting given by the Aphrodisian in his original 
thethreetermsin each of these; thus:— text, though liberally sui^plied by his 

Latin translator. The diagrams of Am- 
monius were long generally employed. 
By Neomagus 1533 (In Trapezimtii Dia- 
lect., f. 35), they are most erroneously 
t y referred to Faber Stapulensis. [See 

Whether these diagrams ascend higher further, Discussions, p. 670. — Ed.] 




APPENDIX. 421 

Syllogistic Figures in general. — " We must premise what 
is the Major Proposition of the Syllogism, and what the Minor. 
But to understand this, we must previously be aware what are 
the Major and Minor Terms. And it is possible to define 
these, both, in common, as applicable to all the three figures 
and, in special, with reference to the first alone. In the latter 
relation, that is, regarding si^ecially the first figure, the Major 
term is that which constitutes the Predicate, the Minor that 
tvhich constitutes the Subject, of the Middle, so far as limited 
to the first figure. But since in neither of the other figures do 
the extremes reciprocally stand in any definite (?) relation to the 
middle term ; it is manifest that this determination is inajDplicable 
to them. We must, therefore, employ a rule common to all the 
three figures ; to wit, that the major term is that predicated, the 
minor that subjected, in the conclusion. Thus, the Major Proposi- 
tion is the one containing the Major Term ; the Minor Propo- 
sition the one containing the Minor Term. Examples : Of the 
First Figure, — Man [t's] animal; animal, substance ; therefore, 
man, substance Of the Second, — Animal [is predi- 
cated] of all man; animal of no stone; man, therefore, of no 
stone. ... Of the Third, — Some stone is white ; all stone 
is inanimate ; cansequenthj, some white is inanimate." . . . 

First Figure.— F. 19 b. 59 ; Aristotle, I. c. § 3. "'But I call 
that the middle term which itself is in another, and another in it ; 
and which in position lies intermediate.' 

" This definition of the middle term is not common to the three 
figures, but limited to the middle of the first figure only. For, 

&c But, if there be a certain difference in species 

between the middle terms of the three figures, they have likewise 
something in common ; to wit, that the middle term is found 
twice in the premises, throughout the three figures ; which also in 
position is middle. For Aristotle wishes in the Diagraph (iu avrrj 
TT) Kara'ypa(f)y) to preserve the order of intermediacy, so that, 
placing the three terms in a straight line, we assign the middle 
place to the middle term. [?] 

Aristotle, I. c. § 4. " ' But [I call] the extremes both that which 
is in another, and that in which another is. For if A be predi- 
cated of all B, and B of all C, it is necessary that A should also be 



422 APPENDIX. 

predicated of all C. We have previously said what we mean by 
the expression [predicated] of all! " 

" It may seem perhaps that this is a [perfect] definition of the 
extremes and of the middle term. But it is not ; for it behoves 
us to sub-understand, in addition, the word only ; and thus the 
definition will rightly run, — But [I call] the extremes, both that 
which is in another [minor], and that in which another is [major] 
For if A be predicated by all B, and B of all C, it is necessary 
that A be predicated of all C. 

" This the first syllogistic mood is of two affirmative universals, 
collecting an affirmative conclusion. Por if B inhere in all C, C is, 
consequently, a part of B. But B is a part of A ; A therefore, 
also, inheres in all C, C being a part of B. The reasoning will be 
j)lainer in material examples — as substance [is predicated] of all 
animal ; animal of all man ; and there is ixdexiedi substance of all 
man; and conversely, a/Z 7?icm {in] animal; all animal substance ; 
therefore, all man substance. 

" But it is manifest how, in this figure, the terms of the first mood 
[Barbara] ought to be taken. The first is the most general, and the 
second the subaltern, genus ; whilst the third is a species more spe- 
cial than the middle. The conclusion ought always to be drawn. 
Thus, if, proceeding synthetically, we commence by the major term 
[and proposition], substance begins ; wherefore it also leads the 
way in the conclusion. [There is predicated] substance of all 
animal (here substance commences) ; animal of all man ; whilst 
the conclusion again commences with substance, — substance of all 
man. But if we start from the minor term [and proposition], as 
from man, with this also the conclusion will commence : all man 
[is] animal ; all animal substance ; all man substance. 

" Aristotle takes the terms A, B, C ; and, from the relation of the 
letters, he manifests to us the order of the first figure. The major 
terra he calls A, because A stands first in order ; the minor term, 
C ; and the middle term B, as B, in its order, follows A, and pre- 
cedes C. 

" It is plain that the terms may possibly be coadequate [and 
therefore reciprocating]; as receptive of science — risible — man; 
for all man is 7'isible ; all risible is receptive of science ; therefore, 
all man is receptive of science." 



APPENDIX. 4j23 

F. 23 b, Aristotle ch. 5, § 2, Second Figure. " ' The major ex- 
treme is that which lies nearer to the middle ; the minor, that 
which lies farther from the middle.' 

" In place of more akin and more proximate to the middle ; not 
in position, but in dignity. For since, of the terms, the middle is 
twice predicated, while, in the conclusion, the major is once pre- 
dicated, but the minor not even once predicated ; [consequent- 
ly], that which is once predicated will be the more proximate to 
that which is twice predicated, that is, to the middle, than that 
which is not even once predicated. Wherefore, we shall hear him 
[Aristotle], in the Third Figure, calling the minor the term more 
proximate to the middle on account of their affinity, for they are 
both subjects, while he calls the major term the more remote. 
Perhaps, also, he wishes that in the diagraph (rfj KaTaypa^rj), 
the major term should be placed closer to the middle, and the 
minor farther off. But the major extreme in this figure, the two 
premises being universal, exists not by nature but by position, for the 
first of the extremes which you meet with as a subject in the second 
figure, — this is the minor extreme, the other is the major. So in 
the example — All man an animal ; no plant animal ; therefore, no 
man plant. In like manner, if we take the commencement from 
plant, this becomes the minor term, and man the major ; as no 
plant animal ; all man animal ; no plant,therefore,man. Con- 
sequently, the major and minor terms exist in these examples, only 
by position, not by nature. If, indeed, one or other of the proposi- 
tions be particular, the major and the minor terms are then determin- 
ed ; for we hold that in this figure the universal is the major." 

Aristotle. — § 3. " 'The middle is placed external to, [not between], 
the extremes, and first in position.' 

" The middle term passes out of what is properly the middle 
position ; it is also placed out of or external to the extremes ; but 
either above these or below. But if it be placed above, so as to be 
predicated of both, it is called first in position ; if below, so as to 
be subjected, it is called second. Wherefore, here, as predicate 
of both premises, he styles the middle term the first ; for if it 
be placed above, it is first in position, and, in being apart from the 
extremes, it is placed without them." 

Aristotle, ch. 6, § 2. Third Figure, f 27, b. " ' The major ex- 



424 APPENDIX. 

treme is that more remote from, the minor is that more proximate 
to, the middle.' 

"The major term in this figure is twice predicated of the middle, 
and in the conclusion ; but the minor once only, and that of the 
middle, for it is subjected to the major in the conclusion ; the 
middle is alone subjected, never predicated. When he, therefore, 
says that the major term is more remote from the middle, he means 
the term always predicate is in affinity more remote from that 
which is never predicate, but always subject. And that which is 
never subject is the major and more proximate term ; that again, 
which is now subject, now predicate, is the minor." 

V. — MAETIANUS CAPELLA.a 

Martianus Capella, De Septem Artihus Liber alihus, L. iv. De 
Dialectica, in capite, Quid sit Predicativus Syllogismus, p. 127, 
ed Grotii ; p. 83, ed Basil. 1582. 

" Hujus generis tres formae [figurse] sunt. 

" Prima est, in qua declarativa [prgedicatum] particula superioris 
sumpti, sequentis efficitur subjectiva [subjectum] ; aut subjectiva 
superioris, declarativa sequentis. Declarativa superioris fit subjec- 
tiva sequentis, ut Omnis voluptas bonum est ; omne bonum utile 
est; omnis igitur voluptas utilis est. Subjectiva superioris fit de- 
clarativa sequentis, si hoc modo velis convertere : Omne bonum 
utile est ; omnis voluptas bonum est; omnis igitur voluptas utilis 
est." 

In First Form or Figure, notices the four direct and five indirect 
moods, — reflexion : and in the second and third, the usual number 
of moods.^ 

In Second Figure — " Hie reflexione si utaris, alius modus non 
efficitur, quoniam de utrisque subjectivis fit illatio." He seems 
to hold that two direct conclusions are competent in Second and 
Third Figures. 

In Second Figure, he enounces generally (four times) as thus : — 

a Flourished A.c. 457, Passow ; 474, See Dialect., Opera, TpTp.BZS, 556, Genev. 

Tennemann. 1650, and above, p. 404. (fl. 520). Cf. 

/3 Cassiodorus, in First Figure, gives Apuleius, Be Syllogismo Categorko, Op., 

both forms, "velsic;" in Second and p. 35. Elmen. (a.c. 160.) Isidorus, of 

Third, though he gives also an " vel sic," Seville, {Gothofr. A uct., p. 878) (a.c. 600 ; 

they ai-e examples, both in converse, of died 636.) 
Capella's general mode of enunciation. 



APPENDIX. 425 

" Omne justum honestum; nullum turpe honestunn; nullum igitur 
justiiTYi turpe ; but sometimes (once) thus, — "Nullum igitur turpe 
justum." 

In Third Form or Figure generally (six times) thus as — " Omne 
justum honestum ; omne justum bonum ; quoddam igitur hon- 
estum bonum ;" but sometimes (once) as, — ^'Quoddam igitur 
bonum JionestuTn." 

VI. — ISIDOEUS. 

Isidorus, Originum, L. i. c. 28. Be Syllogismis Dialecticis. 
Opera, p. 20 (1617) ; in Gothofred. Auctores, p. 878. 

"Formulae Categoricorum, id est, Praedicativorum SyUogis- 
morum sunt tres. Primae formulse modi sunt novem. 

" Primus modus est qui conducit, id est, qui coUigit ex uni- 
versalibus dedicativis dedicativum universale directim : ut, 
Omne justum honestum ; omne honestum bonum ; ergo omne 
justum bonum." All in first figure, with minor first ; in second 
and third figures, varies ; uses per reflexionem et reflexim in- 
difierently ; and through all moods of all figures follows Apuleius. 
" Has formulas Categoricorum Syllogismorum qui plene nosse 
desiderat, librum legat qui inscribitur Perihermenias Apideii, et 
quse subtilius sunt tractata cognosced " 

VII. — AVEEEOES. 

Averroes, In Anal. Prior., L. i., c. v., on First Figure : "If, 
therefore, the middle term be so ordered between the two ex- 
tremes, that it be predicated of the minor and subjected to the 
major, (as, if we say all C is B and all B is A) ; it is plain that 
this order of syllogism is natural to us ; and it is called by Aris- 
totle the first figure." And thus are stated all the examples in detail. 

C vi. Figure Second. — " And the proposition whose subject is 
the subject of the qusesitum is the minor proposition, but that 
whose subject is the predicate of the qusesitum is the major. Let 
us then place first in order of enunciation the minor extreme ; let 
the middle term then follow, and the major come last, to the end 
that thus the major may be distinguished from the minor ; for in 
this figure the terms are not distinguished, unless by relation to 
the qupesitum." So all the examples. 

C. vii. Third Figure. — " That proposition in which lies the sub- 



426 APPENDIX. 

ject of the qusesitura is called the minor proposition, since the 
subject itself is called the minor term ; that proposition which 
contains the predicate of the quassitum is named the major. In 
the example, let the minor term be C, the middle B, and the major 
A, and their order be that we first enounce the middle, then the 
minor, and last of all the major." And so the examples. 

VIII. — Melanchthon. 

Melanchthon, Erotemata Dialecticce, L. iii., p. 175. 

" Demonstration why there are necessarily three [and only three] 
Figures. 

" Every argumentation which admits the syllogistic form, (for of 
such form Induction and Example are not recipient, [?]) proceeds 
either [1°], Erom genus to species universally with an universal 
conclusion, or [2°], From species to genus with a particular conclu- 
sion, or [3°], A distraction of two species takes place, or [4°], There 
is a concatenation of a plurality of causes and effects. Nor are 
there more modes of argumentation, if we judge with skill. 

" The process from genus to species engenders the First Figure. 
And the consequence is valid from the genus with a universal sign 
both affirmatively and negatively to the species,— this is naturally 
manifest. The process from species to genus with a particular 
conclusion engenders the Third Figure. And it is evident that, 
the species posited, the genus is posited. 

" The distraction of species engenders the Second Figure. And 
the reason of the consequence is clear, because disparate species are 
necessarily sundered. These may be judged of by common sense, 
without any lengthened teaching. Both are manifest, — that the 
figures are rightly distributed, and that the consequences are in- 
dubitably valid." 

IX. — Aenauld. 

Arnauld, L'ArtdePenser, {Port Royal Logic), P. iii., ch. 11, p. 
235. — General principle of syllogisms : — " That one of the pre- 
mises should contaifi the conclusion, and the other shoiu that it 
does so contain it." — [So Purchot, Instit.Fhil., Vol. I. P. iii., ch. 1,] 

Ch. v., p. 215. — "Foundation of First Figure. 

" Principle of affirmative moods -.—That what agrees with a 
notion taken universally, agrees also with all of which this notion 
is affirmed ; in other words, with all that is the subject of this 



APPENDIX. 427 

notion, or is comprised within its sphere." [Or, more shortly, 
(says Purchot, c. vi.). Whatever is predicated of the superior, is 
predicated of the inferior.'] 

" Principle of the negative moods : — What is denied of a notion 
taken universally, is denied of all whereof this notion is affirmed!' 
[Purchot — What is repugnant to the superior, is repugnant also 
to the inferior, eh. vL, p. 217.] 

" Foundation of the Second Figure.^' Principle of the syllogisms 
in Cesare and Festino : — That what is denied of a universal 
notion, is denied also of whatever this notion is affirmed, that is 
to say, of all its subjects. 

" Principle of the syllogisms of Camestres, Baroco : — All that is 
contained under the extension of a universal notion, agrees luith 
none of the subjects luhereof that notion has been denied, seeing 
that the attribute of a negative proposition is taken in its whole 
extension." 

Ch. vii. p. 220. " Foundation of the Third Figure. 

" Principle of the affirmative moods : — When two terms may he 
affirmed of the same thing, they may also be affirmed of each 
other, taken particidarly. [So Purchot nearly.] 

"Principle of the negative moods: — When of two terms^ the 
one may be denied, and the other affirmed, oftliesame thing, they 
may be particidarly denied of each other. ^' [So Purchot nearly.] 

No foundation or principle given for the Fourth Figure. 

X. — Grosser. 

Samuelis Grosseri, Pharus Intcllectus, 1697, P. iii., S. i., Mem. 
3, c. 2 (probably from Weiss, see Pref ) " The foundation of the 
first figure is the Dictum De Omni et Nullo ; for whatever is uni- 
versally affirmed or denied of a universal subject, that is also 
affirmed or denied of all and each contained under that subject. 

"The foundation of the second figure is Contrariety; for the 
predicates of contrary things are contrary. 

" The foundation of the third figure is the agreement of the ex- 
tremes in any third ; for what agrees with any third agrees with 
each other, and may be joined or separated in the same proposition, 
inasmuch as they are in agreement or confliction in relation to any 
third thing." 

« Purchot says this Figure rests upon same, hut something agrees tvith the one, 
single principle — 2\vo things are nut the which is repugnant to the other. 



428 APPENDIX. 

Illustrates the three figures by three triangles, p. 132. In 
the first we ascend to the apex on one side, and descend on the 
other ; in the second we ascend at both sides ; in the third we 
descend on both sides. 

XI. — Lambert. 

Lambert, Neues Organon, Vol. I., § 225. — See Melanchthon, 
(above p. 426). 

Relation of Figures. " We further remark that the first dis- 
coverer of Syllogisms and their Figures was, in his arrangement of 
their propositions, determined by some arbitrary circumstance ; his 
views and selections at least were not founded on aught natural and 
necessary (§ 196). He places, to wit, that premise after the other, 
which contains among its terms the subject of the conclusion, pro- 
bably in order to introduce into all the figures a common law. To 
that law, however, we do not restrict ourselves either in speech or in 
writing. The mathematician, who perhaps draws the greatest num- 
ber of formal syllogisms with the fewest paralogisms, commences 
to take the first figure, for example, not with the major but with 
the minor proposition, because not only in this figure is such pre- 
mise always the more obtrusive, but also because its subject is the 
proper matter of discourse. Frequently the premise is only quoted, 
or it is absolutely omitted whensoever it is of itself obvious to the 
reader, or is easily discoverable from the minor and conclusion. 
The conclusion inferred is then, in like manner, constituted into the 
minor proposition of a new syllogism, wherewith a new major is 
connected. This natural arrangement of the syllogisms of the first 
figure, rests, consequently, altogether on the principle, — That tve can 
assert of the subject of an affirmative proposition, whatever we 
may know of its predicate ; or tvhat may he said of the attribute 
of a thing is valid of the thing itself And this is what the syl- 
logisms of the first Figure have peculiar to themselves. It is also 
so expressed ; — What is true of the genus is true also of each of 
its species. 

§ 226. " On the other hand, in the second and third Figures there 
is no talk of species and genera. The second Figure denies the 
subjects of each other, because they are diverse in their attributes; 
and every difierence of attribute is here effectual. We, conse- 
quently, use this figure principally in the case where two things 



APPENDIX. 429 

ought not to be intercommuted or confounded. This becomes 
necessarily impossible, so soon as we discover in the thing A some- 
thing which does not exist in the thing B. We may, consequently, 
say that syllogisms of the second figure lead us to distinguish 
things, and prevent us from confounding notions. And it will be 
also found, that, in these cases, we always use them. 

§ 227. " The third Figure affords Examples and Exceptions; and, 
in this Figure, we adduce all exempla in contrarium. The two 
formula are as follows : — 

"1. There are B %vhich are C; for M is B and C. 

" 2. There are B tuhich are not C / for M is B and not C. 

" In this manner we draw syllogisms of the Third Figure, for the 
most part, in the form of copulative propositions (§ 135) ; because 
we are not wont twice to repeat the subject, or to make thereof 
two propositions. Sometimes one proposition is wholly omitted, 
when, to mt, it is self-manifest. 

"In the Fourth Figure, as in the First, species and genera ap^Dear 
only with this difference, that in the moods, Bai^alvp, Dibatis, 
Fesapo, Fresison, the inference is from the species to the genus ; 
whereas in Calentes there is denied of the species what was denied 
of the genus. For where the genus is not, neither are there any 
of its species. This last mood we, therefore, use when we conclude 
negatively a minori ad majiis, seeing that the genus precedes, and 
is more frequently presented than, any of its species. 

§ 229. " The syllogisms of the four Figures are thus distinguished 
in relation to their employment, in the following respects : — 

" 1. The First Figure ascribes to the thing what we know of its 
attribute. It concludes from the genus to the species. 

" 2. The Second Figure leads to the discrimination of things, and 
relieves perplexity in our notions. 

" 3. The Third Figure affords examples and exceptions in pro- 
positions which appear general. 

" 4. The Fourth Figure finds species in a genus in Baralip and 
Dibatis ; it shows that the sj)ecies does not exhaust the genus in 
Fesapo, Fresison ; and it denies the species of what was denied 
of the genus in Calentes. 

§ 230. " This determination of the difference of the Four Figures 
is, absolutely speaking, only manifested when we employ them 
after natural fashion, and without any thought of a selection. For, 



430 APPENDIX. 

as the syllogisms of every figure admit of being transmuted into 
those of the first, and partly also into those of any other, if we rightly 
convert, or interchange, or turn into propositions of equal value, 
their premises ; consequently, in this point of view, no difference 
subsists between them ; but whether we in every case should perform 
such commutations, in order to bring a syllogism under a favourite 
figure, or to assure ourselves of its correctness, — this is a wholly 
different question. The latter is manifestly futile. For, in the 
commutation, we must always undertake a conversion of the pre- 
mises, and a converted proposition is assuredly not always of 
equal evidence with that which we had to convert, while, at the 
same time, we are not so well accustomed to it ; for example, the 
proposition. Some stones attract iron, every one will admit, be- 
cause The magnet is a stone, and attracts iron. This syllogism is 
in the Third Figure. In the first, by conversion of one of its pre- 
mises, it would run thus : — 

Major, — All magnets attract iron ; 
Minor, — Some stones are magnets ; 
Conclusioa, — Some stones attract iron. 

Here we are unaccustomed to the minor proposition, while it ap- 
pears as if we must pass all stones under review, in order to pick 
out magnets from among them. On the other hand, that the 
magnet is a stone, is a proposition which far more naturally sug- 
gests itself, and demands no consideration. In like manner, A 
circle is not square; for the circle is round, — the square not. This 
proof [in the third figure] is as follows, when cast in the first : — 

What is not round is no circle ; 
A square is not roimcl ; 
Consequently, &c. 

Here the major proposition is converted by means of terminus infi- 
nitiis, and its truth is manifested to us only through the conscious- 
ness that all circles are rcmnd. For, independently of this pro- 
position, should we not hesitate, — there being innumerable things 
which are not round, — whether the circle were one of those which 
belonged to this category ? We think not ; because we are aware. 
§ 231. " It is thus apparent that we use every syllogistic figure 
there, where the propositions, as each figure requires them, are 
more familiar and more current. The difference of figures rests. 



APPENDIX. 431 

therefore, not only on their form, bnt extends itself, Ly relation to 
their employment, also to things themselves, so that we use each 
figure where its use is more natural : The first for finding out or 
'proving the Attributes of a thing ; the second for finding out or 
proving the Difference of things ; the third for finding out and 
proving Examples and Exceptions ; the fourth for finding out 
and excluding the Species of a Genus. 

§ 232. " Further, whether the three last figures are less evident 
than the first, is a question which has been denied [affirmed (?)] on 
this account, that the first figure only rests immediately on the 
Dictum de Omni et Nulla [§ 220], whilst the others have hitherto, 
by a circuit, been educed therefrom. We have already remarked 
[§ 211], that this circuit, through our mode of notation, is wholly 
superseded. We need, therefore, only translate its principle into 
the vernacular, and we shall find that the Dictum, de Omni et Nulla 
is on that account applicable to the first figure, because its truth 
is based on the nature of the proposition. From this principle, 
therefore, the first figure and its moods admit of an immediate de- 
duction ; it is thus only a question whether the other figures are 
incapable [capable (?)] of such immediate deduction, or whether it 
is necessary previously to derive them through the first figure ? 
Our mode of notation shows that the latter is an [unnecessary] cir- 
cuit, because every variety of syllogism admits for itself a various 
notation, and because, in that case, the j^remises are taken for what 
they actually are. Consequently, every figure, like the first, has its 
own probation, — a probation drawn exclusively from the natures of 
the propositions. The whole matter is reduced to this, — Whether 
a notion, wholly or in part, is, or, wholly or in part, is not, under 
a second ; and whether, again, this second, ivh oily or in part, is, 
or, wholly or in part, is not, under a third. All else proceeds only 
on the interchange of equivalent modes of expression, — the figured, 
namely, and those which are not figured. And this interchange 
we may style translating, since the figured modes of expression may 
be regarded as a special language, serving the purpose of a nota- 
tion. We have above (§ 220), after all the syllogistic modes were 
discovered and denoted, adduced the Dictum de Omni et Ntdlo, 
but only historically, since our manner of determining the syllogis- 
tic moods is immediately founded on the nature of the propositions, 
from which this Dictum is only a consequence. Moreover, this 



432 APPENDIX. 

consequence is special, resting, as it does, on the notions of Species 
and Genera. Wherefore, its validity only extends so far as pro- 
positions can be recalled to these notions ; as, for example, in 
the First Figure. In the Second, the notion of Difference emerges ; 
and in the Third, the notion of Example. If we, therefore, would 
have special dicta for the several Figures, in that case it would 
follow, and, at the same time, become manifest that the middle 
term of a syllogism, considered for itself, expresses, in the First 
Figure, a principle [of Ascription or Procreation^ ; in the Second, 
Difference ; in the Third, an Example; and in the Fourth, the 
principle of Reciprocity. 

1. For the First Figure. Dictum de Omni et Nullo. What is 
true of all A, is true of every A. 

2. For the Second Figure. Dictum de Diverso. Things which 
are different, are not attributes of each other. 

3. For the Third Figure. Dictum de Exemplo. When we find 
things A which are B, in that case some A are B. 

4. For the Fourth Figure. Dictum de Reciproco. I. If no M 
is B ; then no B is this or that M. II. If C is [or is not] this or 
that B ; in that case some B are [or are not] C." 

XII. — Platner. 

Platner, Philosophische Aphorismcn, 3d ed., 1793. — Part I., § 
544, conformed to his Lehrhuch der Logik und Metaphysik, 1795, 
§ 227. " The reason why the predicate belongs to the subject is in 
all possible syllogisms this, — because the subject stands in a relation 
of subordination with, [is either higher or lower than], a third 
notion to which the predicate belongs. Consequently, all inference 
proceeds on the following rule : — If the subject of the [concluding] 
judgment stand in a relation of subordination with a third notion, 
to which a certain predicate pertains ; in that case, this predicate 
also pertains to the same judgment, affirmatively or negatively." 

In his note on this Aphorism, Platner {Lehrhuch) admits — "My 
fundamental rule is only at fault in the second Aristotelic figure, 
which, however, is no genuine figure ; because here, in the pre- 
mises, the subject and predicate have changed places," &c. In the 
2d edition of his Aphorisms (1784) he had adopted the principle of 
Identity with the same third, as he has it : " In what extension 
or proportion (Maasse) two notions are like or unlike to a third, 



APPENDIX, 433 

in the same extension or iwopoi'tion are they like or unlike each 
other." (§ 628.) 

Philosophische Aphorismen, Part I., third edition, 1793, 
§ 568, compared with second, 1784, § 672-676. — " Nevertheless, 
each of these grammatical figures of syllogism has its peculiar 
adai^tation in language for the dialectical aj^plication of proofs ; 
and the assertion is without foundation, that the first is the most 
natural. Its use is only more appropriate, when we intend to show, 
— that a p)redicate pertains \or does not jiertain'] to a subject in 
virtue of its class. More naturally than in the first, do we show, 
in the second, the difference of things apparently similar ; and in 
the third, the similarity of apparently different things. The 
fourth figure, [it is said in the second edition], on account of the 
position of its terms, is always unnatural in language." 

Philosophische Aphorismen, Parti., last edition, 1793, § 561. — 
" The principle of the first figure is the Dictum de Omni et Nullo.'" 

§ 564. — " Touching the other figure, [the third, for in this edi- 
tion Platner abolishes, in a logical relation, the second], its special 
principle is the following rule : — What belongs to the subordinate, 
that, since the subordinate is a part of the universal, belongs also 
in jKirt {particularly) to the universal." 

In the second edition, 1784, the second figure is recognised, 
and, with the third, obtains its special law. 

§ 659. — " The principle of the second figure is : — // tiuo notions, 
wholly or in part, are opposite to a third, so are they also, wholly 
or in part, op)posite to each other." 

§ 664. — "The principle of the third figiu'e is : — What can he 
jxirticulaidy affi^rmed or denied of a subaltern species.^ that also, 
in so far as such subaltern species is part of a genus, may be 
p)articidarly affirmed or denied of the genus." 

Philosophische Aphoi^ismen. Part I., § 546. Note. — " In 
general, logicians treat the subject as if it were necessarily subordi- 
nated to the predicate. It may, however, on the contrary, be the 
higher notion, and the predicate thus be subordinated to it. This 
is the case in all particular propositions where the predicate is not 
an attribute of the genus, but an accident of the subject. For 
instance, — Some creatures are animals; here the subject is the 
higher : Somie men are imperfect ; here the higher is the predi- 
cate. We must not, therefore, in our syllogistic, thus enounce the 

VOL. II. 2 E 



434 APPENDIX. 

fundamental rule of reasonings, — If the subject he subordinated to 
a third notion, but with or in the relation of subordination with 
a third notion^ 

XIII— Fries. 

Fries, System der Logik, § 56. — " The species of categorical syl- 
logisms are determined by tlie variety of relations in which three 
notions may stand to each other, so that a syllogism may be the 
result. 

" These relations may be thought as three. 

" Case I. — Three notations are reciprocally subordinated in gra- 
dation, so that the second is subordinated to the first, but super- 
ordinated to the third. 

" Case II. — Two notions are subordinated to a third. 

" Case III. — Two notions are superordinated to a third.'' 

" When, in these cases, is a syllogism possible ? 

§ 57. — " In all the three cases, the syllogisms are equally valid, 
for they are fomided on the general laws of the comiection of 
notions. 

" They all follow, to wit, from the relation of a whole sphere to 
its parts, which lies in the Dictum de Omni et Nullo. The prin- 
ciples for the three mentioned cases are thus : — ■ 

" For the first, — The part (C) of the part (B) lies in the whole 
(A), and what (A) lies out of the whole (B), lies also out of the 
part (C). 

" For the second, — What (A or some A) lies out of the whole (B), 
lies also out of its parts (C). 

" For the third, — If a part (B) lie in two wholes (A and C), in 
that case these have a part in common; and if a part (B) lie in a 
whole (C), but out of another whole (A), in that case the first (C) 
has apart out of the other (A). 

" The first case alone coincides immediately with the perfect de- 
claration of a syllogism, — that a case is therein determined by a 
rule. For the third case, therefore, our two declarations of a 
major premise, — that it is the rule, and that it contains the major 
term, — do not coincide, seeing that here the minor term may be 
forthcoming in the rule. On this account, the arrangement of the 

« [See Jordano Bruno (in Denzinger, § 237, p. 163]. 
Logik, t. ii., p. 259). Stattler, Logica, 



APPENDIX. 435 

first case is said to be the only regular, and the others are reduced 
to it. That this reduction is easily possible, we may in general 
convince ourselves, by reflecting that every syllogism requires a 
general rule as premise, and that the other cases are only distin- 
guished from the first by the converted arrangement of the propo- 
sitions. But as all propositions may be either purely converted or 
purely counterjiosed, consequently the two last cases can at most 
so far deviate from the first, that they are connected with the first 
case only through reversed {gegentheilige) notions. 

§ 57 b. " The doctrine of the several species of categorical syllo- 
gisms, as regulated by the forms of their judgmeuts, is at bottom 
an empty subtlety ; for the result of all this circuity is only, that, in 
every categorical syllogism, a case is determined by a rule, and this 
is already given in the law, that in every reasoning one premise 
must be universal. The scholastic logic treats of this doctrine 
only in so far as the species of syllogism are determined by the 
forms of judgment, and thereby only involves itself in long gram- 
matical discussions. Aristotle has been falsely reproached for 
overlooking the fourth figure, he only having admitted three. For 
Aristotle proceeds, precisely as I have here done ; only on the rela- 
tion of notions in a syllogism, of which there are possible only our 
three cases. His error lies in this, — that he did not lay a general 
rule at the root of every figure, but, with a prolixity wholly useless, 
in determining the moods of the several figures, details each, 
even of the illegitimate, and demonstrates its illegitimacy. This 
prolixity has been too often imitated by other logicians, in the 
attempts at an evolution of the moods. Kant, goes too far, in de- 
nouncing this whole doctrine as a mere grammatical subtlety. The 
distinction of the three cases is, however, a logical distinction ; and 
his assertion, that the force of inference in the other two is wholly 
derived from that of the first case, is likewise not correct. I mani- 
festly, however, conclude as easily in the third case, — 'A part 
which lies in two wholes, is a part common to both,' — as in the 
first, — 'The part of the part lies in the whole.' The third case 
presents, indeed, the readiest arrangement for reasonings from the 
particular to the general, i. e., for syllogisms in the second figure 
according to our terminology. 

" The scholastic doctrine of the four syllogistic figures and nine- 
teen moods of categorical syllogisms requires no lengthened illus- 



436 APPENDIX. 

tration. If the figures are determined by the arrangement of 
notions in the premises, then the following combination is exhaus- 
tive. For the conclusion in all cases S P [being supposed the 

same], the [terms or] notions stand : 

1) According to our first case, M P 

S M 

2) With converted major premise, P M 

S M 

3) With converted minor premise, M P 

M S 

4) Both premises converted, P M 

M S 

" Should we therefore simply convert both jjremises in a syllo- 
gism of the first figure, we are able to express it in all the figures. 
Let the notions given be fireproof] lead, metal, there then follows 
the conclusion — Some metal is not fireproof— from, the premises : — 

In the First Figure — iVo lead is fireproof ; 

tSome 7netal is lead ; 
In the ^QQOixOLY\gwxQ^Not]img fireproof is lead ; 

Some metal is lead ; 
In the Third Figure — No lead is fitrj^roof; 

A II lead is metal ; 
In the Fourth YigViVQ— Nothing fireproof is lead, 

All lead is metal. 

" It is here apparent that the three first figures are oui' three 
cases ; but the fourth we did not employ, as it contains no peculiar 
relations or notions, but only under our first case superordinates, 
and then subordinates a middle term. This manner of enunciating 
a syllogism is thus only possible, where we are competent, through 
conversions, to transmute the arrangement of the first figure into 
that of the fourth. Now this happens : 1] If we convert the con- 
clusion S P into P S, since then the major and the minor 

terms, as also the major and minor premises, change names; or, 2] 
If both premises allow of an immediate conversion, so that the one 
remains universal ; for then the converted propositions contain the 
same thoughts as those given, and, consequently, establish the same 
conclusion." 

[Objections to Fries' doctrine of figure — 1°, Only applies to affir- 
matives ; 2°, Only the arrangement of the results of a successful 
comparison, and takes no heed of the comparisons that may have 



APPENDIX. 437 

been fruitless, (the illegitimate moods) ; 3°, Takes accomit of only 
one subordination, for, in second and third cases, in each there is 
a reciprocal subordination in Extension and Comprehension.] 

XIV and XV. — Keug and Beneke — theie Docteines of 
Syllogism ceitigised. 

The authority" of the two following philosophers, who conclude 
this series, is rather negative than j)Ositive ; inasmuch as they 
both concur in proving, that the last attempts at a reformation of 
the Syllogistic Theory proceed on a wholly different ground from 
that on which, I think, this alone can be accomplished. These two 
philosophers are Krug and Beneke ; for, beside them, I am aware 
of no others by whom this has been attempted. 

Krug was a disciple of the Kantian school, Kant's immediate 
successor in his Chair of Logic and Metaphysics at Koenigsberg, 
and, subsequently, Professor of Philosophy in the University of 
Leipsic. He is distinguished, not only as a volmninous writer, but 
as a perspicuous and acute thinker ; and his peculiar modification 
of the Kantian system, through a virtual return to the principle of 
Common Sense, is known, among the German theories, by the 
name of Synthetism. His Logic, (the first part of his System of 
Theoretical Fhilosoj^hy), was published in 1806, and is one of the 
best, among the many excellent, treatises on that science, which we 
owe to the learning and ability of the Germans. (I have before me 
the fourth edition, that of 1833.) Krug propounded a new theory 
of syllogistic ; but the novelty of his scheme is wholly external, 
and adds only fresh complication to the old confusion. It has, 
accordingly, found no fiivour among subsequent logicians. 

Passing over the perverse ingenuity of the principles on which 
the whole doctrine is founded, it is enough to state, that Krug dis- 
tributes the syllogistic moods into eight classes. Of these the first, 
(which, with some other logicians, he considers not as a figure at all, 
but as the pure, regular, and ordinary form of reasoning), corre- 
sponds to the First Figure of the Aristotelico-Scholastic distribu- 
tion. The other seven classes, as so many impure, irregular, and 
extraordinary forms, constitute, (on the analogy of Rhetoric and 
Grammar), so many figures. Of these, the new is only the old 
First Figure, the minor premise, in extension, being stated before 
the major. Krug, like our other modern logicians, is not aware 



438 APPENDIX. 

that this was the order in which the syllogism was regularly cast, 
in common language, by the Greeks, by the Arabians, by the Jews, 
and by the Latins prior to Boethius." The old and new first figures 
are only a single figure, the syllogism being drawn in the counter 
orders of breadth and of depth. A mood in these orders, though 
externally varying, is intrinsically, — is schematically, — the same. 
Krug's distinction of his new first figure is, therefore, null. Thus, 
Barama is Barbara; Caleme isCelarent; Dirami is Darii; Firemo 
is Ferio. Nor is his discrimination of the other six better founded. 
His new (the old) Second, and his FiftJt Figures, are also one. 
The latter is precisely the same with the former ; Fimeso is 
Festino, and Fomaco is Baroco. In one case, (under Camestres), 
Krug adopts, as alone right, the conclusion rejected by the logi- 
cians. In this, he and they are, in fact, both wrong ; though in 
opposite ways. Each mood, in the second, (as in the third), figure, 
has two indifferent conclusions ; and the special one-sided practice 
of the former is only useful, as gainsaying the general one-sided 
precept of the latter. The same objection applies to Krug's new 
(the old) Third, in connection with his Sixth Figure. They are 
one ; Daroco is Bocardo, Fapimo is Felapton, and Fisemo is 
Ferison. In two cases, (under Disamis and Bocardo), Krug has 
recognised the repudiated conclusion. Krug (§ 109) has, how- 
ever, committed an error in regard to Bocardo. He gives, as its 
example, the following syllogism, in which, for brevity, I have 
filled ujj the quantifications : 

" Some animals are not [an//] viviparous ; 
All animals are [some] orcjanised things ; 
Therefore, some organised things are not [ani/] viinparous." 

In a note, he adds : " The conclusion should here be : — ' There- 
fore, some things which are not viviparous are [some] organised.' 
And this is seen also by reduction. We have, however, followed 
the arbitrary precept of the logicians, that the extreme in the 
second proposition should stand subject in the conclusion ; although 
it be here indifferent, which extreme becomes the subject. The 
conclusion is only changed into another quality." Only changed 
into another quality ! Only an affirmative conclusion from a 
negative premise ! The legitimate inference is : — 

a See above, p. 403. — Ed. 



APPENDIX. 439 

" Therefore, no vivijmrous is some organic ; " or, 
" Therefore, any viviparous is not some organic.^' 

Bachmann, [Logik, § ] 35), anotlier eminent logician, has erred 
with Krug. A particular predicate in a negative proposition, seems 
indeed one of the last difficulties for reformed logic. Krug's new 
(the old) Fourth Figure bears a corresponding relation to his 
Seventh. He is right, certainly, in abolishing all the moods of the 
fourth figure, except Fesapo and Fresiso ; and, from his point of 
view, he is hardly to be blamed for not abolishing these likewise, 
along with the correlative moods, Fapesmo and Fi^isesmo, and, 
with them, his seventh figure. Finally, rejecting the scholastic 
doctrine of Reduction, he adopts, not without sundry perverse 
additions, Kant's jjlan of accomplishing the same end ; so that 
Krug's conversive and contrapositive and transpositive interpola- 
tions, by which he brings back to propriety his sevenfold figured 
aberrations, are merely the substitution of one " false subtlety " for 
another. He, and Bachmann after him, renounce, however, " the 
crotchet of the Aristotelians," in making the extreme of the prior 
premise the predicate, always, of the conclusion, in the first and 
second figures ; and, though both do this partially and from an 
erroneous point of view, their enunciation, such as it is, is still 
something. 

Professor Beneke, of Berlin, is the last to whom I can refer, 
and in him we have, on the point in question, the final result of 
modern speculation. This acute and very original metaphysician 
stands the uncompromising champion of the philosophy of experi- 
ence, against the counter doctrine of transcendentalism, in all its 
forms, now prevalent in Germany ; and, among the other depart- 
ments of mental science, he has cultivated the theory of reasoning, 
with great ability and success. In 1832 appeared his Lehrhuch 
der Logik, &c.; in 1839, his Syllogismorum Analyticorum Ori~ 
gines et Or do Naturalis, &c. ; and in 1842, his System der Logik, 
&c., in two volumes. In Logic, Beneke has devoted an especial 
share of attention to the theory and distribution of Syllogism ; but 
it is precisely on this point, though always admiring the ingenuity 
of his reasonings, that I am compelled overtly to dissent from his 
conclusions. 



440 APPENDIX. 

The Syllogistic of Beneke is at once opposed, and correspondent, 
to that of Krug ; there is an external difference, but, without imi- 
tation, an internal similarity. Instead of erroneously multiplying 
the syllogistic figures, like the Leipsic philosopher, the philosopher 
of Berlin ostensibly supersedes them altogether. Yet, when con- 
sidered in essence and result, both theories agree, in being, and 
from the same side, severally, the one an amplification, the other 
an express doubling, of the nineteen scholastic moods. In this, 
both logicians were unaware, that the same had been, long ago, 
virtually accomplished in the progress of the science ; neither con- 
sidered, that the amplification he proposed was superficial, not to 
say mistaken ; and that, instead of simplicity, it only tended to 
introduce an additional perplexity into the study. Beneke has the 
merit of more openly relieving the opposition of Breadth and 
Depth, in the construction of the syllogism ; and Krug, though on 
erroneous grounds, that of partially renouncing the old error of 
the logicians in regard to the one syllogistic conclusion, in the 
second and third figures. But, in his doctrine of moods, Beneke 
has, I think, gone wrong in two opposite ways : like Krug, in his 
arbitrary multiplication of these forms ; like logicians in general, 
in their arbitrary limitation. 

In regard to the former, — the counter quantities of Breadth and 
dej)th do not discriminate two moods, but merely two ways of 
stating the same mood. Accordingly, we do not multiply^ the 
moods of the first figure, to which alone the principle applies, by 
casting them in the one dependency and in the other; we only 
show, that, in that figure, every single mood may be enounced in a 
twofold order, more german, the one to the quantity of extension, the 
other to the quantity of intension. An adequate notation ought, 
equally and at once, to indicate both. But in reference to the 
second and third figures, the case is worse. For in them we have 
no such dependency at all between the extremes ; and to double 
their moods, on this principle, we must take, divide, and arbitrarily 
appropriate, one of the two indifferent conclusions. But, as every 
single mood of these figures has a double conclusion, this division 
cannot be made to difference their plurality. If Professor Beneke 
would look (instar omnium) into Apuleius or Isidorus, or, better 
than either, into Blemmidas, he will find all his new moods, (not, 



APPENDIX. 441 

of course, those in tlie fourth figure) stated by these, as by other 
ancient logicians ; wlio, however, dreamed not that the mere acci- 
dental difference of, what they called, an analytic and synthetic 
enounceraent, determined any multiplication of the moods them- 
selves. 

In the latter respect, Dr Beneke has only followed his predeces- 
sors ; I, therefore, make no comment on the imperfection. But, in 
accomplishing what he specially proposes, whilst we do not find 
any advancement of the science, we find the old confusion and 
intricacy rej^laced by another, perhaps worse. To say nothing of 
his non-abolition of the fourth figure, and of his positive failures 
in doubling its moods ; the whole process is carried on by a series 
of arbitrary technical operations, to supersede which must be the 
aim of any one who would reconcile Logic with nature. His new 
(but which in reality are old) amplifications are brought to bear 
(I translate his titles) through " Commutations of the Premises, — 
by Subalternation, — by Conversion, — by Contraposition ; " and "of 
the Major, — of the Minor," — in fact of both premises, {e.g. Fesajw, 
&c.). And so difficult are these j^rocesses, if not so uncertain the 
author's language, that, after considerable study, I am still in doubt 
of his meaning on more points than one. I am unable, for ex- 
ample, to reconcile the following statements : — Dr Beneke repeatedly 
denies, in conformity with the common doctrine, the universal 
quantification of the predicate in affirmative propositions ; and yet 
founds four moods upon this very quantification, in the conver- 
sion of a universal affirmative. This is one insolubility. But there 
arises another from these moods themselves (§ 28-81). For, if we 
employ this quantification, we have moods certainly, but not of the 
same figure with their nominal correlatives ; whereas, if we do not, 
simply rejecting the permission, all slides smoothly, — we have the 
right moods in the right figure. This, again, I am unable to solve. 
Dr Beneke's duplication of the moods is also in sundry cases only 
nominal ; as is seen, for example, in Ferio 2, Fesapo 2, and Fre- 
siso 2, which are forms, all, and in all respects, identical. I must 
protest also against his violence to logical language. Thus, he 
employs everywhere "non omne," "non omnia," "alle sind nicht," 
&c., which is only a particular, (being a mere denial of omnitude), 
for the absolute or universal negative, " nullum," " nulla," " kein 



442 APPENDIX. 

ist," no, none, not any, &c., in opposition both to principle, and to 
the practice of Aristotle and succeeding logicians. 



[XVI.— TiTius. 

Gottlieb Gerhard Titius, Ars Gogitandi, sive Scientia Cogita- 
tionum Gogitantium, Gogitationibus Necessai^is Instructa et a 
Peregrinis Liherata. Leipsise, 1723, (first edition, 1701). 

Titius has been partially referred to by Sir W. Hamilton, as 
having maintained the doctrine of a Quantified Predicate. See 
above, p. 312. His theory of the Figure and Mood of Syllogism 
is well deserving of notice, — proceeding, as it does, on the applica- 
tion of that doctrine. This theory is principally contained in the 
following extracts from his Ars Gogitandi, which show how closely 
he has approximated, on several fundamental points, to the doc- 
trines of the New Analytic.'^ 

Titius gives two canons of syllogism : — 

I. Affirmative. " Qusecunque conveniunt in uno tertio, ilia 
etiam, juxta mensuram illius convenientise, inter se conveniunt." 

II, Negative. " Qusecunque pugnant in certo aliquo tertio, ilia, 
juxta mensuram illius disconvenientise, etiam inter se pugnant." 
C. ix. §§ 30, 27. 

The following relates to his doctrine of Figure and Mood, and 
to the special rules of Syllogism, as commonly accepted : — 

C. X. § i. " Sic igitur omnium Syllogismorum formalis ratio in 
genuina medii termini et prpedicati ac subject! Conclusionis colla- 
tione consistit ; eam si dicere Ye\\ii forniam essentialem, aut figu- 
ram generalem vel communem, non valde reluctabor. 

§ ii. " Prseter eam vero Peripatetici Figurxis ex peculiari medii 
termini situ adstruunt, ea ratione ut Primani figuram dicant, in 
qua medius terminus in Majore est subjectum, in Minore Prredica- 
tum, Secundam, ubi idem bis prsedicati, et Tertiam, ubi subjecti 
locum bis subit. Galenus adjecit Quartam primes contrariam, in 
qua medius terminus in majore est prredicatura, in minore subjec- 
tum, quam pluribus etiam exposuit Autor. Art. Gog. p. 3, c. 8. 

a. For Titius' doctrine of a Quantified thetical Syllogism, see .above, pp. 312, 
Predicate, its application to the Conver- 274, 375.- Ed. 
sion of Propositions and to the Hypo- 



APPENDIX. 443 

§ iii. " Cseterum illae figurse tantura sunt accidentales, ab iisque 
vis conchidendi iion dependet. Quodsi tamen quis diversum medii 
termini situm attendendum esse putet, turn nee Quarta figura negii- 
genda esse videtur, licet earn Peripatetici nonnulli haut curandam 
existiment, vide Ulman. Synops. Log. 1. 3, c. 2, p. J 64. 

§ iv. " Interim Pi^ima Cfeteris magis naturalis ex eo videri 
potest, quod Subjectum et Prsedicatum Conclusionis in Prsemissis 
suam retineat qualitatem, cum in secunda et tertia alterum quali- 
tatem suam exuere, in quarta vero utrumque earn deponere debeat. 

§ V. " Postea in unaquaque figura, pro ratione quantitatis et quaii- 
tatis propositionum, peculiares Modi adstruuntur, ita quidem ut 
Primje figuree Qiiatuor, totidem Secundse, Terti?e sex attribuantm-, 
ex quibus etiam debite variatis Quarta quinque accipiat, prout ilia 
passim cum vocabulis memorialibus recenseri solent, ut ilia quidem 
hue transcribere opus non sit, vide Autor, Art. Cogit., p. 3, c. 5, 
6, 7, 8. 

§ vi. "Non opus esse istis figuris et modis ad dijudicandam 
Syllogismorum bonitatem, ex monito § 3, jam intelligi potest. 
Quomodo tamen sine iis bonitas laudata intelligi queat, id forte 
non adeo liquidum est 

§ vii. " Non diu hie quserenda sunt remedia : Observetur forma 
essentialis seu figura communis, ac de veritate Syllogismi recte 
judicabitur. Applicatio autem hujus moniti non est diflicilis, nam 
primo rcspiciendum ad conclusionem, deinde ad medium terminum, 
quo facto etiam j udicari potest, an ejus et terminorum conclusionis 
collatio in prsemissis recte sit instituta nee ne 

§ ix. " De c?etero uti anxie jam non inquiram, an omnis bene 
concludendi ratio numero modorum denario circumscribatur, 
quod quidem juxta aKpi^eiav mathematicam demonstrasse videri 
vult Autor. Art. Cog. p. 3, c. 4, ita id haut admiserim, quod illi 
modi, quos vulgo laudant. Primes, Secundse aut Tertiag figurse prae- 
cise sint assignandi, licet hoc itidem acumine matheraatico se de- 
monstrasse putet dictus Autor. d. I. c. 5 seqq. 

§ X. " Cum enim qusevis propositio possit converti, modo quan- 
titas prssdicati probe observetur, hinc necessario sequitur, quod 
quivis Syllogismus, adhibita propositionum conversione, in quavis 
figura possit proponi, ex quo non potest non sequalis modorum 



444. APPENDIX. 

numeriis in unaquaque figiira oriri, licet ilK non ejusdem semper 
sint quail titatis. 

§ xi. " Operas pretium non est prolixe per omnia Syllogismorum 
singulis figuris adscriptorura exempla ire, sufficiat uno assertionem 
illustrasse, v. gr. in prima figura, modo Barbara liic occurrit Syllo- 
gismus apud d. Autor. c. 5. 

0. Sapiens suhjtcitur voluntati Dei, 

0. Ilonestus est sajnens, 

E. 0. honestus suhjicitur voluntati Dei. 

§ xii. " Hunc in secimda figura ita proponere licet : 

Quidam, qui suhjicitur voluntati Dei, est omnis sapiens, 

Omnis honestus est sapiens, 

E. Omnis honestus suhjicitur voluntati Dei, 

ratio concludeiidi maiiet eadein, sapiens enim et is qui suhjicitur 
voluntati Dei, uniuntur in Majore, dein sapiens et Honestus in 
Minore, ergo in conclusione idea sapientis et Ejus qui voluntati 
Dei suhjicitur, quoque conveniunt. 

§ xiii. " In tertia figura ita se habebit : 

0. Sapiens suhjicitur voluntati Dei, 

Q. Sapiens est omnis honestus, 

E. 0. honestus suhjicitur voluntati Dei, 

nec in liac concludendi ratione aliquid desiderari potest, nam me- 
dius terminus universaliter unitur cum conclusionis pr?edicato, 
deinde, quantum sufficit, conjungitur cum ejusdem subjecto, seu 
omni honesto, ergo subjectum et pnedicatum se quoque mutuo 
admittent. 

§ xiv. " Cseterorum eadem est ratio, quod facile ostendi posset, 
nisi tricas illas vel scribere vel legere tsediosum foret. Ex liis 
autem sequitur, quod omnes regulce speciales, quce niodis vidgari- 
hus attemperatce vulgo circumferuntur,falsce sint, quod sjieciatim 
ostendere liceat. 

§ XV. " In uiiiversum triplici modo impingitur, vel enim conclu- 
sio creditur absurda, qucB talis non est, vel vitiuni est in materia, 
ac altera proimissaruni falsa, vel adsunt qiiatuor termini, adeo- 
que alisurditas conclusionis, si aliqua subest, nunquam ab ea causa 
dependet, quam referunt regulas. 



APPENDIX. 44d 

§ xvi. " Sed videamus distinctius, (1) major in jprima figura 
semper sit univeralis 

§ xvii. " Inflectam hue exemplum minus controversum, quod 
Autor, Art. Cog. p. 3, c. 7, in modo Disaniis, tertise figurse, pro- 

ponit : 

Quldam impii in honore hahentur in micndo, 

Quidam vituperandi sunt omnes i7npii, 

E. quidam vituperandi in honore hahentur in viundo. 

§ xviii. " Hie habes primam figuram cum majore partieulari, 
optime iterum coneludentem, nam licet medius terminus particu- 
lariter sumatur in majore, ejus tamen ille est capacitatis, ut in 
eodem convenientia prsedicati et subjecti ostendi queat, et nisi hoc 
asset, nee in tertia figura rite coneluderetur. 

§ xix. " Nee valde obsunt, quse vulgo illustrandse regules addu- 
cuntur. Ex sententia Weis. in Log. p. i., lib. 2, c. 2, § 4, male ita 

concluditur : 

Q. animal volat, 
0. Leo est animal, 
E. Q. Leo volat. 

Verum si animal sumitur in minore sieut in majore, tum ilia falsa 
est, si vero alio sensu, tum existunt quatuor termini ; his ergo 
causis, non particularitati Majoris, vitiosa conelusio tribuenda. 
§ XX. " Nam alias ita bene concluditur : 

Q. animal volat, 

0. avis est animal, (illud quoddam), 

E. 0. avis volat, 

nam licet medius terminus jiarticularis sit, tantae tamen est latitu- 
dinis, ut cum utroque Conelusionis termino possit uniri. 

§ xxi. " Porro (2) Minor semper sit affirmans. Sed quid desi- 
derari potest in hoc Syllogismo : 

0. Homo est animal rationale, 

Leo non est homo, 

E. non est animal rationale ? 

et nonne ilia ratio concludendi manifesto bona est, quas subjectum 
et prsedicatura, quae in certo tertio non conveniunt, inter se quoque 
pugnare contendit ? 

§ xxii. " Sed ais, mutemus paululum Syllogismmn et absurditas 
conelusionis erit manifesta : 



446 APPENDIX. 

0. Homo est miimal, 

Leo non est homo, 

E. Leo non est animal ! 

Verum si terminus animalis in Conclusione perinde sumitur, sicut 
suppositus fiiit in majore, nempe particular iter, turn conclusio est 
verissima ; si autem aliter accipiatur, turn evadunt quatuor termini, 
quibns adeo, non negationi Minoris, absiirditas conclusionis est 
imputanda, qiise observatio in omnibus exemplis quae hie objici 
possunt et solent, locum habet. 

§ xxviii. " Sed revertamur ad regulas vulgares ! Nimirum (3) 
In secunda fi[/ura major sit universalis. Verum cur non ita 
liceat concludere : 

Quidam dives est Saxo, 

Quidam Germanus est omnis Saxo, 

E. Quidam Germanus est dives 1 

quod argumentum Weis. 1. 2, c. 4, § 2, intuitu tertiee figurae pro- 
ponit. 

§ xxix. " Argumenta, quae fallere videntur, v. gr. quod Weisius 
1. 2, c. 3, § 3, profert : 

Quidam homo est sapiens, 
JVidlus stulfus est sapiens, 
E. Nullus stultus est homo, 

et similia, responsione, § 22, data eliduntur ; nimirum conclusio vel 
non est absurda, si recte intelligatur, vel adsunt quatuor termini, 
quibus adeo, non particularitati majoris, vitium est imputandum. 

§ XXX. " Amplius (4) Ex jniris ajirmativis in secunda jigura 
nihil concluditur, sed rairum foret, si ilia concludendi ratio falleret, 
quae fundamentum omnium Syllogismorum affirmativorum tam 
evidenter prae se fert ! Hoc argumentum utique formaliter bonum 

est : 

Omnis sapiens sua sorte est contentus, 
Paidus sua sorte est contentus, 
E. Paulus est sapiens. 

§ xxxi. " Sed fallunt multa argumenta, v. gr. Weisio d. c. 8, § 
3, adductum : 

Omnis lepiis vivit, 

Tu vivis, 

E, Tu es lepus, 



APPENDIX, 447 

verum non falliint ob affirmationem prflemissariim, sed quia vel 
minor falsa est, si scil. prpedicatum accipiatur eodem sensu, quo in 
Majore sumtum est, vel quia adsunt quatuor termini, si prsedicatum 
Minoris particulariter et alio sensu accipiatur. 

§ xxxii. " Non possunt etiam vulgo diffiteri, quin ex puris affir- 
mativis aliquando quid sequatur, verum id non v'lformce sed ma- 
terice fieri causantur, vide Ulman. Log. 1. 3, c. 3, § 4. Hsec vero 
est petitio principii, nam qu?e conveniunt in uno tertio, ilia etiam 
inter se convenire debent, idque non fortuito, sed virtute nnionis 
laudatae, seu beneficio formse. 

§ xxxiv. " In tertia figura (5) Minor semper sit affirmans. 
Ego tamen sic recte concludi posse arbitror : 

Quoddam laudandum est omnis virtus, 
JVuNum hiudanduvi est qucedam magnificentia, 
E qucedam magnificentia non est vij-tus. 

§ XXXV. " Nee valde urgent exempla opposita Weisius d. 1. 2, c. 
4, § 2, hoc affert : 

Omnis homo ambulat, 

Nidlus homo est porcus, 

E. quidavi 2)orcus non ambulat, 

nam recurrit responsio § 22 data, quae vel conclusionem falsam 
non esse, vel causam falsitatis a quatuor terminis dependere osten- 
dit, qu^ etiam locum haberet, licet conclusionem universalem, 
Nidlus porcus amhidat, assumas. 

§ xxxvi. " Tandem (G) In tertia figura conclusio semper sit 
particidaris. Verum Syllogismum cum conclusione universaK, 
jam exhibui § 13, in Exemplis autem quae vulgo afiferuntur, v. g7\ 

Omnis senator est ho7ioratus, 

Omnis senator est homo, (quidam sell.), 

E. omnis homo est honoratus, 

vide Weis. d. 1 2, c. 4, § 3, occurrunt quatuor termini, (nam homo, 
in minore particulariter, in conclusione universaliter sumitur), qui 
adeo veram absurdse conclusionis causam, ac simul regulse vulgaris 
falsitatem ostendunt. 

§ xxxvii. " Ilia autem omnia, quse contra vulgares regulas 
hactenus disputavimus, non eo pertinent, quasi rationem conclu- 



44-8 APPENDIX, 

dendi rejiciendis regulis liinc iiide coiifectam commendemus, ita 
ut in demonstrationibiis eadem iiti, aut valde delectari debeamus. 
Quin omni potius eo spectaiit, ut Peripateticos, qui formani Syllo- 
gismorum essentialem vel omnino non vel nimis frigide exponunt, 
in explicandis etiani eorum figuris accidentalibus, falli probarem. 

§ xxxix. " Atque ex hactenus dictis etiam intelligi potest, quae 
nostra de Reductione sit sententia. Nimirum ex nostris hypothe- 
sibus ilia nihil aliiid est, quam SijUogismorum 'per omnes quatiior 
fignras accidentales, salva semper conclusione, facta variatio. 

§ xl. " Pertinet igitur ilia tantum ad Frcemissa, Syllogismus 
enim semper ut instrmnentuni veritatis inquii-endae considerari, 
adeoque queestio probanda, qua3 semper immobilis sit, nee, prout 
visum est, varietur, prjesupponi debet. 

§ xli. " Keductionis unica Lex est, ut simpliciter, juxta figuroa 
indolem, propositiones convertamus, quod sine ulla dijSicultate pro- 
cedit, dummodo quantitatem subjecti et prsedicati debite confidere- 
mus, ceu ex iis quae de Conversione diximus satis liquet. 

§ xlii. " Finis est, ut per ejusmodi variationem, terminorum 
unionem vel separationem eo accuratius intelligamus, hinc omnis 
utilitas reductioni non est abjudicanda, si enim recte instituatur, 
ingenium quantitati propositionum observandce magis magisque 
assuescit, ac inde etiam in penitiorem format esseutialis intelligen- 
tiam provehitur. 

§ xliii. "In vuhjari i?efZ((C^io?ie, qu^e in libellis logicis passim 
exponitur, vide Aut. Art. Cog. p. 3, c. 9, quasdam exempla repre- 
liendi non debent, quando v. g. Gesare ad Gelarent reducitur, nam 
ibi simplici conversione alicujus propositionis defunguntur, juxta 
legem, quam § 41, reductioni dedimus. 

§ xliv. " Sed si ab illis exemplis abeas, parura vel nihil est, 
quod in eadem laudari debeat, dum fere ex falsis liypothesibus 
omnis reductio oritur, nam conversio p>Gr contrapositionem pras- 
supponitur, quam tamen valde dubiam esse, supra ostendimus, 
praeterea peculiares modi in singidis figuris adstruuntur, ac omnis 
reductio ad p>rimam figuram facienda, esse existimatur, cum tamen 
idem Syllogismus per omnes figuras variari queat. 

§ xlv. " Ipsa vero reductio nullis legibus adstricta est, converti- 
tur Conclusio, transponuntur Prremissje, propositiones negativte 
mutantur in affirmativas, atque ita quidvis tentatur, modo figura 



APPENDIX. 449 

intenta obtineatur. Quo ipso puerilis error, quo Logica, pro arte 
concinnandi tres lineas, easque in varias formas mutandi habetur 
satis elucet. luepta scientia est, quoe in verbis disponendis, circum- 
agendis aut torquendis unice, occupatur. 

§ xlvi. " Juxta haec igitur, vulgar! modo reducere, maximam 
partem nihil aliud est, quam errorem errore tegere, ingenia discen- 
tium torquere, ac magno conatu magnas nugas agere, inscitiamque 
professa opera ostendere." — Ed.] 



D. SYLLOGISTIC MOODS. 

(Vol. I. p. 401.) 

(a) Direct and Indieect Moods. 
(1) Theie Principle. — First and Fourth Figure. 

(See above, Vol. I, p. 423.) 

Direct and Indirect Moods, — principle of. — That the two terms 
should hold the same relation to each other in the conclusion, that 
they generally hold to the middle term in the premises. This de- 
termined by the Question. This constitutes direct, immediate, 
natural, orderly inference. When reversed, by Conversion, there 
emerges indirect, mediate, unnatural, irregular inference. 

In the two last Figures, (Second and Third), the two terms hold 
the same relation to the middle term in the premises ; ergo no 
indirect inference, but always two direct conclusions possible. 

In the first Figure, as the two terms are subordinated to each 
other in the premises, one direct conclusion from premises, 
whether read in Extension or Comprehension, and, consequently, 
an indirect one also, — the First Figure being first figure in Exten- 
sive quantity ; the Fourth Figure being first figure in Comprehen- 
sive quantity. Direct and indirect moods in each. 

1. Blunder about definition of major and mmor terms by logi- 
cians, (for which Aristotle not responsible)," cause of fancy of a 
Fourth Figure, constituted by indirect moods in comprehension. 

2. That predicate could have no prefinition, and, therefore, though 

ci.'&ee^iah\,[NotcB etAnimadversiones tographo edttce cura Caspari Posneri 
in Compendium Dialecticum T). Conradi Prof. Pub. Jena;. 1656, Ad. L. iii. c. 
Horneii, nunc primum ex Auctoris An- viii.] 

VOL. II. 2 F 



450 APPENDIX. 

they allowed its converse, the direct inference was not suffered. 
This in Fapesmo, Frisesmo, (these alone, by some logicians, ad- 
mitted in the First Figure), and Fesapo and Fresison in Fourth or 
Comprehensive First, a 

3. That major proposition, that which is placed first. 



Fourth Figure. — The First Figure, and that alone, is capable of 
being enounced in two orders, those of Breadth and of Depth. It 
is exactly the same syllogism in either order ; and, while the order of 
Depth was usually employed by the Greeks, Orientals, and older 
Latins, that of Breadth has been the common, if not the exclusive, 
mode of enouncement among the western logicians, since the time 
of Boethius. In either form, there are thus four direct moods, 
and five indirect, — in all nine moods ; and if the Figure be held to 
comprise the moods of either form, it will have eighteen moods, as 
in fact is allowed by some logicians, and, among others, by Men- 
doza, (Disj). Log. et Met. T. I. pp. 515, 516), Martianus Capella, 
{De Septem Artihus Liber alihiis, L. iv., De Dialectica, in cap. 
Quid sit Prcedicativus Syllogismus, (see above, p. 424), states 
and allows either form, but, like his contemporaries, Greek and 
Latin, he employs in his examples the order of Depth. 

Now, mark the cajDrice of the logicians of the west subsequent 
to Boethius. Overlooking entirely the four direct moods in the 
order of Depth, which they did not employ, as the conclusion 
would, in these cases, have been opposed to their own order ; they 
seized upon the five indirect moods of the order of Depth, as this 
afforded a conclusion corresponding to their own, and constituted 
it, thus limited, into a Fourth Figure. 

Did not make two forms of First Figure. 

An indirect conclusion is in subject and predicate the reverse of 
a direct ; opposed, therefore, to the order of predication marked 
out by the premises which the direct conclusion exclusively follows. 

a [That foui-thFigui-e differs from first § 3, p. 29. Campanella, Phil. Sat. 
only by transposition of Premises,— held Dialect., Lib. ii. c. vi. art. xi. p. 391, 
by Derodon, Loyica Restituta, p. 606. and art. iv. p 385, (1635). Ridiger, De 
Camerarius, Disputationes Philosophicce, Sensu Veri et Falsi, ii. 6, § 36. Criisius, 
Disp. i., qu. 13, p. 116. Caramuel, Rat. Weg Zur Geicissheit, § 335, p. 606. Plat- 
ed Real. Phil., Disp. xii. p. 45. Ircnasus, ner, Philosophische Aphorismen, i. § 554, 
Iitte/j. Phil., Ehnienta Lor/!re.i, Sect. iii. p. 267.] 



APPENDIX. 



451 



An indirect conclusion, (what the logicians have not observed)," is 
an inference from the dkect conclusion, and, therefore, one mediate 
from the premises. 



(2) Moods of Fourth Figure redressed. 
(Early Pajier — previous to 1844. Later signs of quantity sub- 
stituted. — Ed.) 
I. Bamalip, — only Barbara with transposed premises and con- 
verted couclu.sion. 

(2) All irons are (some) metals ; 
(1) All metals are (some) minerals ; 

All irons are {some) minerals. 
(By conversion.) 

Some minerals are (all) irons. 




(Minerals) , 



■ : (Metals) , 
(Redressed) 



: (Irons). 




II. Calemes, — only Celarent with transposed premises and con- 
verted conclusion. 

(2) All snails are (some) mollusca ; 
(1) No molluscum is any insect ; 

No snail is any insect. 
(By conversion) 

No insect is any snail. 



(Insect) : 



; (Molluscum) , m : (Snail) 

(Redressed) 

III. Dimatis, — only Darii with transposed premises and con- 
verted conclusion. 

« But see Contarenus, De Quarta Figura Syllog., Opera, p. 235. — Ed. 




452 



APPENDIX. 



(2) Some stars are {some or all) planets ; 

(1) All jjlanets are some things moving round sun 

Some stars are sotne things moviny round sun ; 
(By conversion) 

Some things moving round sun are some stars. 




{Moving round Sun), 



: {Planets) : , 
(Redressed) 



, {Stars) 



IV. Fesapo, [Felapos]." 

(2) iVo ai-tery is any vein ; 

(l) All veins are {some) bloodvessels 

No artery is {some) bloodvessel. 
(By conversion) 

Some bloodvessel is no artery. 




{Bloodvessels) , 



M : ( Vei7i) : - 
(Redressed) 



: (.1 rfery) 




V. Fresison, [Frelilos]. 



(2) No muscle is any nerve ; 

(1) Some nerves are {some) expansion on hand 

No muscle is {some) expansion on hand. 
(By conversion) 

Some expansion on hand is no muscle. 




^ Zabarella, Opera Logica, Be Quarta verses premises and reduces to Fapesmo 
Fig. Syll, pp. 118,119,125. Burgers- an indirect mood of First; thusviolat- 
dyk, Instit. Lor/., L. ii. c. 7, p. 167, re- ing the rule of that Figure. 



APPENDIX. 453 

{Expansion mi hand), m , (N'erve) : | m : {Muscle) 

(Redressed) 



(March 1846.) — My universal law of Figured Syllogism excludes 
the Fourth Figure. — What worse relation of subject and jwedicate 
subsists between either of tiuo terms and a common third term 
with which one, at least, is positively related ; that relation sub- 
sists between the two terms themselves. What relation, &c. ; that 
relation, &c. Now, in Fourth Figure, this is violated ; for the predi- 
cate and subject notions, relative to the middle term in the pre- 
mises, are in the conclusion turned severally into their opposites 
by relation to each other. This cannot, however, in fact be ; and, 
in reality, there is a silently suppressed conclusion, from which 
there is only given the converse, but the conversion itself ignored. 

Fourth Figure. Reasons against — 

1°, Could never directly, naturally, reach (a) Conclusion from pre- 
mise, or (b) Premises from quresitum. 

2", All other figures conversion of premises of First, but, by 
conversion of conclusion, (as it is), no new figure. 

3°, All other figures have one conclusion Fom-th a converted 
one, often dijBFerent. 

(March 1850.) — Fourth Figure. The logicians who attempt to 
show the perversion in this figure, by speaking of higher and 
lower notions, are extra-logical. Logic knows nothing of higher 
and lower out of its own terms ; and any notion may be subject 
or predicate of any other by the restriction of its extension. 
Logic must show the perversion in this Figure ex facie syllogismi, 
or it must stand good. On true reason, why no Fourth Figure, 
see Ai-istotle, Anal. Pr., L. i., c. 23, § 8, and Pacius, in Commen- 
tary. 

(March 1850.) — Fesapo and Fresiso, (also Fapesmo, Frisesmo), 
proceed on the immediate inference, unnoticed by logicians, that 
the quantities, apart from the terms, may, in propositions InA and 
AnI, be converted. 



454? APPENDIX. 

Averroes on Prior Analytics, B. i., Ch. 8. 

" If we ask whether A be in C, and say that A is in C, because 
A is in B, and B in C ; in this case, there is a natural syllogism 
by general confession ; and this in the First Figure. 

" In like manner, if we say that A is not in C, because B is in 

C, and B is not in A ; it is plain that we collect that conclusion by 
natural process ; and this is the Second Figure, which is frequently 
found employed by men in their ordinary discourse. 

" In like manner, also, if we say that A is in C, because A and C 
are in B ; that syllogism is also natural to us, and is the Third 
Figure. But if we say A is in C, because C is in B, and B in A ; 
the reasoning is one which no one would naturally make ; for the 
reason that the quajsitum, (that is, C to be in A), does not hence 
follow, — the process being that in which we say A is in C, since A 
is in B, and B in C ; and this is something which thought would 
not perform, unless in opposition to nature. From this it is mani- 
fest, that the Fourth Figure, of which Galen makes mention, is not 
a syllogism on which thought would naturally light," (&c.) There- 
after follows a digression against this figure. See also the same 
book, Ch. 23d, and the Epitome, by Averroes, of the same, Ch. i. 

(3) Fourth Figure. — Authorities for and against. 
Admitted by — 
Ildefonsus de Penafiel, Cursus Philosophicus, Disp. Summul. 

D. iii. p. 89. G. Camerarius, Disput. Philos., P. i., q. xiii., p. 116. 
Po7't B.oyal Logic, p. iii. c. 8, and c. 4. Ridiger, De Sensu Vei'i et 
Falsi, L. ii., c. 6, § 36. Hauschius in Acta JErud. p. 470 ct seq. 
Lips. 1728. 'Noldms, Logica Recognita, c. xii. p. 277. Crakan- 
thorpe, Logica, L. iii. c. xv. p. 194, (omitted, but defended). 
Lambert, JS^eues Organon, I. § 237, et seq. Hoffbauer, Analytik 
der Urtheile und Schliisse, § 138. Twesten, Logik, inshesondere 
die Analytik, § 110. Leibnitz, Opera, ii. 357; v. 405 ; vi. 216, 
217, ed. Dutens. Oddus de Oddis, (v. Contarenus, Non Pari 
Quart. Fig. SylL, Opera Omnia, p. 233, ed. Venet, 1589.) 

Eejected by — 

Averroes, In. An. Prior., L. i. c. 8. Zabarella, Opera Logica, 
De Quarta Fig. SylL, p. 102 et seq. Purchot, Instit. Phil. T. I. 
Log. P. iii. c. iii. p. 169. Molinaeus, Flementa Logica, L. i. 
c. viii. Facciolati, Rudinienta Logica, P. iii. c. iii. p. 85. Scay- 



APPENDIX. 



455 



nus, Paraphrasis in Organ., p. 574. Timpler, Logicce Systema, 
L. iv, c. i. qii. 13, p. 543. Platner, Philosophische Aphorismen, 
I. p. 267. Burgersdicius, Instit. Log. L. ii. c. vii. p. 165. Dero- 
don, Logica Restituta, p. 606. Wolf, Phil. Rat, § 343, et seq. 
(Ignored.) Hollmann, Logica, § 453, p. 569. Goclenius, Pi^o- 
hlemata Logica, P, iv., p. 119. Keckermann, Opera, T. I., Syst. 
Log. Lib. iii., c. 4, p. 745. Ai'riaga, Cursus Philosophicus, In 
Summulas, D. iii. § 5, p. 24. Aristotle, An. Prior, i. c. 23, 
§ 8 ; c. 30, § 1, (omitted). Jo. Picus Miraudulanus, Conclusiones, 
Opera, p. 88. Melanchthon, in 1st edition of Dialectic, L. iii., 
De Figuratione, (1520), afterwards (1547), restored, (Heumanni, 
Acta, iii. 753). Cardinalis Caspar Contarenus, Epistola ad Oddum 
de Oddis, De Quart. Fig. SylL Opera, p. 233 (1st ed., 1571). 
Trendelenburg, Elementa Logica, § 28, &c. Herbart, Lehrbiich 
der Logik, Einleit., 3, § 71. Hegel, Encyclopcedie, § 187. Pries, 
System der Logik, § 57 b. Griepenkerl, Lehrbuch der Logik, § 
29 et seq. Drobisch, Logik, § 77, p. 70. Wallis, Institutio Logicce, 
L. iii. c. ix. p. 179. 

(6) INDIKECT MOODS OF SECOND AND THIRD FIGUEES.a 



From 


(II. 


Fig.) 




i. 


/Cesare 
^Cumestres 




Reflexim ; (1, 2, 5, 8, 9) p, Cesares. 


ii. 




Reflexim ; (2, 5, 8, 9.) Camestre, Ca- 








mestres, Faresmo, (only subaltern of 








Camestres) ; rejected (2), admitted 








(3, 6.) 


iii. 


Festino 




Premises reversed ; (2, 3, 4, 5, 6, 7, 8, 9.) 
Firesmo, Frigeros, 


iv. 


Baroco 




Premises reversed ; (2, 5, 7, 8, 9.) Bo- 
cardo, Moracos, Forameno. 




(III. 


Fig.) 




i. 


Darapti 




Reflexim; (1, 2, 3, 4, 10, 11.) 


ii. 


Felaptou 




Premises transposed ; (4, 5, 6, 7, 8, 9, 
11.) Fapemo, Fapelmos. 


iii. 


/Disamis 
\Datisi 




Reflexim; (4, 7, 10, 11.) 


iv. 




Reflexim ; (4, 7, 10, 11.) 


V. 


Bocardo 




Premises transposed ; (4, 7, 9, 11.) Ba- 
roco, Macopos, Danorcoc. 


vi. 


Ferison 




Premises transposed ; (4, 5, 6, 7, 8, 9, 








11.) Frisemo, Fiseros. 



a The indirect Moods of the First to the authorities given on following 
Figure are universally admitted. page. — Ed. 

/8 The numbers within brackets refer 



456 



APPENDIX. 



(TI. Fig.) 
Mart. Capella 
Duns Scotus 



3. Lovaniciises, (1535) 

4. ! Pacius, (1584) 



Conimbricenses 



9. 
10. 



11. 



Burgersdicius, (1626) 
Caramuel, (1642) 
Scheibler, (1653) 
Noldius, (1666) 



Cesare, reflexim. 

Cesare and Camestres, conclusions simp- 
ly converted ; Festino and Baroco. 
Rejects (and rightly), what has since 
been called Faresmo, as a mere sub- 
altern of Camestres {An. Pr. L. i. qu. 
23. See also Conimbricenses, In 
Arist.Dial. II. p. 362.) 

Faresmo, Firesmo. 

Firesmo (oa An. Pv. L. i. c. 7, and rela- 
tive place of his Com. Anal.) 

Record that indirect moods from Cesare 
and Camestres ; and also Friseso, Bo- 
cardo were admitted by some " re- 
centiores" (II. p. 362.) 

Faresmo, Firesmo. 

Moracos, Frigesos. 

Cesares, Camestres, Firesmo, Bocardo. 

Cesares, Camestre, Firesmo, Forameno ; 
(he has for the direct mood Facrono, 
in place of Baroco.) 



(III. Fig.) 
Apuleius 
Cassiodorus 
Isodorus 
Duns Scotus 



Lovanienses 

Pacius 

Conimbricenses 



Burgersdicius 

Caramuel 

Scheibler 



Noldius 



Darapti, reflexim. 
Do. 
Do. 

Darapti, Disamis, and Datisi, their con- 
clusions simply converted; Felapton, 
Bocardo, Ferisou, {Sup. An. Pr., L. 
i. qu. 24.) 

Fapemo, Frisemo (ib.) 

Fapemo, Frisemo (ib.) 

Record that some " recentiores" admit 
indirect moods from Darapti, Disa- 
mis, Datisi ; also Fapesmo, Frisesmo, 
and Baroco. 

Fapemo, Frisemo. 

Fapelmos, Macopos, Fiseros. 

Admits them from Disamis, Datisi, Da- 
rapti, but not from those which con- 
clude particular negations. 

Danorcoc, (he has for Bocardo Docam- 
roc), Frisemo, Fapemo, and what are 
converted from Darapti, Disamis, and 
Datisi without names. 

Darapti virtually two moods ; this 
maintained by Theophrastus. 



APPENDIX. 



457 



Indirect moods are impossible in the Second and Third Figures, 
for what are called indirect conclusions are only the direct conclu- 
sions. Mem., that in the Second Cesare and Camestres are vir- 
tually one ; whilst in the Third Figure Darapti is virtually two, as 
Disamis and Datisi are one. 

For the particular quantification of the Predicate, useful illus- 
trations, as in the First from Fapesmo, Frisesmo, or (in the pseudo 
Fourth) from Fesapo and Fresiso ; so in the Second Figure from 
what have been called the indirect moods of Figure II. 



1. Bocardo. 



2. Firesmo. 



1. Baroco. 



2. Fapemo. 



2. Frisemo. 




(1853.) Blunders of Logicians. — What have been called the 
Indirect Moods of the Second and Third Figures, arise only from 
the erroneously supposed transposition of the premises ; and the 
Fourth Figure is made up of the really indirect moods of the First 
Figure, with the premises transposed. 



(c) New Moods — Notes upon Table of Syllogisms-o 

Fig. I. vi. — Corvinus, {Institution es Philosophice Rationalis, 
1742, § 540), says : — " There sometimes appears to be an inference 
from pure particulars. For example, Soinie learned are [_some'] 
ambitious men ; some men are [all the] learned ; therefore, some 

a See below, Appendix xi. — Ed. 



458 APPENDIX. 

men are ambitious. But the minor proposition, althougli formally 
particular, involves, however, a universal, to wit, its converse, — All 
the learned are[^some^ men, — which is equipollent." — Why not, then, 
scientifically enounce, (as I have done), without conversion, what 
the thought of the convertend already really and vulgarly involved? 

In all Figures. — I have been not undoubtful, whether the 
syllogisms of the class, in which the two premises, being the 
same, are mutually interchangeable, should be regarded as a single 
or as a double mood. Abstractly considered from all matter, the 
mood is single ; for the two premises, however arranged, afford 
only a repetition of the same form. But so soon as the form is 
applied to any matter, be it even of a symbolical abstraction, the 
distinction of a double mood emerges, in the possible interchange 
of the now two distinguished premises. To the logicians this ques- 
tion was only presented in the case of Darapti (III. ii.) ; and on this 
they were divided. Aristotle [An. Pr. i. c. 6, § 6) contemplates 
only one mood ; but his successor, Theophrastus, admitted two, 
(Apuleius, De Hah. Doctr. Platonis, L. iii. OjJ. p. 38, Elm). Aris- 
totle's opinion was overtly preferred by Alexander, {ad locum, £ 30, 
ed. Aid. quoted above, p. 419), and by Apuleius, [1. c.) ; whilst that 
of Theophrastus was adopted by Porphyry, in his lost connnentary 
on the Prior Analytics, and, though not without hesitation, by 
Boethius, (De Syll. Gateg. L. ii.. Op. pp. 594,598, 601, 604). The 
other Greek and Eoraan logicians silently follow the master; from 
whom, in more modern times, Valla (to say nothing of others) only 
differs, to reduce, on the counter-extreme, Cesare and Camestres, 
(II. ix. a, and X. b), and, he might have added, Disamis and Datisi, 
(III. iv. v.), to a single mood, [De Dial., L. ii. c. 51). (For the ob- 
servations of the Aphrodisian, see above p. 415 et seq.) 

To me it appears, on reflection, right to allow in Darapti only a 
single mood ; because a second, simply arising through a first, and 
through a transposition, has, therefore, merely a secondary, cor- 
relative, and dependent existence. In this respect all is differ- 
ent with Cesare and Camestres, Disamis, and Datisi. The prin- 
ciple here applies in my doctrine to the whole class of syllogisms 
with balanced middle and extremes. 

Fig. II. xii. b. — David Derodon, [Log. Rest. De Arg., c. ii. § 51), 



APPENDIX. 459 

in canvassing the special rule of the Second Figure, — that the 
major premise should be universal, — he now approbates, he now 
reprobates syllogisms of this mood ; but wrong on both alterna- 
tives, for his admissions and rejections are equally erroneous. " Hie 
syllogismus non valet; — Aliquod animal est [aliquod^ rationale ; 
sed [idlus] asinus non est [idlus^_^ rationalis ; ergo, [uUus] asinus, 
non est [aliquod] animal." (P. 63.5.) The syllogism is valid ; only 
it involves a principle which Derodon, with the logicians, would 
not allow, — That in negatives the predicate could be particular, — 
(see Log. Rest. De Argument, c. ii. § 28, p. 623.) Yet almost 
immediately thereafter, in assailing the rule, he says : — " At multi 
dantur syllogismi constantes majori particular!, qui tamen sunt 
recti; ut, — Aliquod animal non est [idlus'] lapis; sed [omnis] 
adamas est [aliquis] lajns; ergo, \idlus] adamas non est [aliquod] 
animal." (This syllogism is, indeed, II. iii. a ; but he goes on :) 
"Item: Aliquod animal est [aliquod] rationale; sed [idlus] 
lapis non est [tdhis] rationalis ; ergo [ullus] lapis non est [ali- 
quod] animal." Now these two syllogisms are both bad, as in- 
ferring what Derodon thinks they do infer, — a negative conclusion 
with, of course, a distributed predicate, (p. 623) ; are both good, 
as inferring what I suppose them to infer, — a negative conclusion 
Avith an undistributed predicate. 

Fig. III. viii. b. — Derodon, {Ibid, § 54), in considermg the 
Special Rule of the Third Figure, — that the minor premise should 
be affirmative, — alleges the following syllogism as "ritious:" — 
"Omnis homo est [aliquod] animal; sed [tdlus] homo non est 
[ullus] asinus; ergo, [ullus] asinus non est [aliquod] animal," 
(p. 638.) It is a virtuous syllogism, — with a particular predicate 
(and not a universal, as one logician imagines), in a negative con- 
clusion. — Again, (omitting his reasoning, which is inept), he pro- 
ceeds : — " Hie vero syllogismus non est vitiosus, sed rectus : — 
[Omnis] homo est [quidam] rationalis ; sed [ullus] homo non est 
[ullus] asinus [or Deus] ; ergo [ullus] asinus [or Deus] non est 
[quidam] rationalis." This syllogism is indeed correct ; but not, 
as Derodon would have it, with a distributed predicate in the con- 
clusion. That his conclusion is only true of the asinus, per acci- 
dens, is shown by the substitution of the term Deus; this showing 
his iUation to be formally absurd. 



460 APPENDIX. 

Fig. III. ii. — Derodon {Ibid.) says : — " Denique, conclusionem 
in tertia figura debere esse particularem, non imiversalem, sta- 
tuunt commimiter Philosophi ; unde hie syllogismus non valet ; 
— ' Omnis homo est [quidanij rationalis ; sed omnis homo est 
[quoddaml animal; ergo, omne [quoddam'] animal est [quoddam] 
7'ationale. Verum, licet conclusio sit universalis, syllogismus 
erit bonus, modo," &c., (p. 638.) The syllogism is, and must 
remain, vitious, if the subject and predicate of the conclusion be 
taken universally, whilst both are undistributed in the antecedent. 
But if taken, as they ought to be, in the conclusion, particularly, 
the syllogism is good. Derodon, in his remarks, partly overlooks, 
partly mistakes, the vice. 

Derodon, criticising the Special Eule of the First Figure, — that 
the major premise should be universal, — says, inter alia : — " At 
multi dantur syllogismi primre figure constantes majori particu- 
lari, qui tamen sunt recti : ut, — ' Aliquod animal est [aliquod^ 
rationale; sed homo est [aliquod^ animal; ergo [!!] homo est 
aliquis] rationalis': item," &c., &c., (p. 627.) This syllogism is 
vicious ; the middle term, animal, being particular in both its 
quantifications, affords no inference.* 



XI. 

LOGICAL NOTATION. 

(See Vol. I., p. 305.) 

(a) Lambert's Linear Notation.^ 

This very defective, — indeed almost as bad as possible. It has 
accordingly remained unemployed by subsequent logicians ; and 
although I think linear diagrams do afford the best geometrical 
illustration of logical forms, I have found it necessary to adopt a 

a See above, p. 317. — Ed. bert and Eulcr, see S. Maimon, Versuch 

$ For Lambert's scheme of notation, einer neiten Logih, Sect, iv., § 7, p. 64 ct 

see bis Neiies Organon, I. § 21. ; and seq, Berlin, 1794. — Ed. 

fur a criticism of the schemes of Lam- 



APPENDIX. 461 

method opposite to Lambert's, in all that is peculiar to him. I 
have been unable to adopt, unable to improve, anything. 

1°. Indefinite or particular notions can only be represented by 
the relation of two lines, and in two ways : 1°, One being greater 
than the other ; 2°, One being partially out of relation to the 
other. Instead of this, Lambert professes to paint particularity by 
a dotted line, i. e., a line different by an accidental quality, not 
by an essential relation. But not even to this can he adhere, for 
the same notion, the same line, in different relations, is at once 
Tiniversal and particular. Accordingly, in Lambert's notation, the 
relation of particular notions is represented sometimes by a conti- 
nuous, sometimes by a dotted, line, or not represented at all. (See 
below, I* 1, 2,3, 4, 5). 

2°, The inconsistency is seen at all climax in the case of the 
predicate in affirmatives, where that term is particular. In Lam- 
bert's notation it, however, shows in general as distributed or uni- 
versal ; but in this he has no constancy. (See 1*, 1, 2, 3, 4). But 
the case is even more absurd in negative propositions, where the 
predicate is really taken in its whole extent, and yet is, by the 
dotted line, determinately marked as particular. (See 4). 

3°, The relation of negativity, or exclusion, is professedly re- 
presented by Lambert in one line beyond, or at the side of, another. 
This requires room, and is clumsy, but is not positively erroneous : 
— it does express exclusion. But his affirmative propositions are 
denoted by two unconnected lines, one below the other. This is 
positively wrong ; for here the notions are equally out of each 
other as in the lateral collocation. But even in this he is incon- 
sistent ; for he as often expresses the relation of negativity by 
lines in the relation of higher and lower. (See below, 1, 4). 

4°, He attempts to indicate the essential relation of the lines by 
the fortuitous annexation of letters, the mystery of which I have 
never fathomed. 

5°, He has no order in the relation of his lines. 

The middle term is not always the middle line, and there is no 
order between the extremes. 

This could not indeed be from his method of notation ; and ex- 
cept it be explained by the affixed letters, no one could discover 
in his lines the three compared notions in a syllogism, or guess at 
the conclusion inferred. (See 1 — 5). 



462 APPENDIX. 

6°, From poverty the same diagram is employed to denote the 
most different moods in affirmative and negative. (Compare 2 
and 3 with 4). 

7°, No order in the terms in the same figure. 

8°, Incomplete. Lambert can represent ultra-total, &c., included 
in affirmative, but not ultra-total, excluded in negative. Has the 
merit of noticing this relation. 

9", Lambert ; but it is needless to proceed. What has been 
already said, shows that Lambert's scheme of linear notation is, in 
its parts, a failure, being only a corruption of the good, and a 
blundering and incongruous jumble of the natural and conven- 
tional. The only marvel is, how so able a mathematician should 
have propounded two such worthless mathematical metliods. But 
Lambert's geometrical is worse even than algebraic notation. 

To vindicate what I have said, it will be enough to quote his 
notation of the moods of the Third Figure, (I. p. 133), which I 
shall number for the previous references. 



1.* Darapti. 



1. Felapton. 



2. Disamis. 



3. Datisi. 



4. Bocardo. 



5. Ferison. 



HI. F 


IGUKE. 






. C- 


■ c 






M 


Ill 






. B— 


1) 






M 


m 


0- 


c 


B- 


b 






B- 





b 




M 


. . C . 


m 




C- 
M 


. B . . 


c 
111 




B- 





— 


b 


M 


C . . . 


in 




M- 


— mC 
B . . . 


— - 


— c 



APPENDIX. 4(53 

(h) Notation by Maass. 

Professor Maass of Halle « discontented, not unreasonably, with 
the geometrical notations of Lambert and Euler, has himself pro- 
posed another, compared with which, those of his predecessors 
show as absolutely perfect. It will be sufficient to despatch this 
scheme, with a very few remarks. To use it is wholly impossible ; 
and even the ingenious author himself has stated it towards the 
conclusion of his Logic (§ 49o — 512), in the course of which, it is 
not, (if I recollect aright), honoured with a single reference. It is 
however, curious, as the only attempt made to illustrate Logic, 
not by the relations of geometrical quantities, but by the relations 
of geometrical relations, — angles. 

1°. It is fundamentally wi'ong in principle. For example, 
Maass proposes to represent coinclusive notions, notions, there- 
fore, to be thought as the same, by the angles of a triangle, which 
.cannot possibly be imaged as united, for surely the identity of the 
concepts, triangle, trilateral, and figure with angles equal to two 
right angles, is not illumined by awarding each to a separate 
corner of the figure. On the contrary, coexclusive notions he 
represents by angles in similar triangles, and these can easily be 
conceived as superposed. The same may be said of co-ordinates. 
But, waving the objection that the difierent angles of a figure, as 
necessarily thought out of each other, are incapable of typifying, 
by their coincidence, notions to be thought as coinclusive, — it is 
further evident, that the angles of an equilateral triangle cannot 
naturally denote reciprocal or wholly identical notions, in contrast 
to others partially identical ; for every angle of every triangle 
infers, — necessitates, — contains, if you will, — the whole of every 
other, equally as do the several angles of an equilateral triangle. 

2°. But Maass is not consistent. He gives, for instance, a tri- 
angle, (Fig. 12), to illustrate the subordination of one notion to 
another ; and yet he represents the lower or contained notion by 
an obtuser, the higher or containing notion by an acuter, angle. 

3°. The scheme is unmanifest, — in fact, nothing can be less ob- 
trusive. It illustrates the obscure by the obscure, or, rather, it 

« Oriindriss der Lor/llc, 1793. I quote ing in the way I do of Maass' scheme of 
from the fourth edition, 1823. I regret notation ; for his Logicis one of the best 
the necessity imposed on me of speak- compends published even in Germany. 



4G4- APPENDIX. 

obscures the clear. Requiring itself a painful study to compre- 
hend its import, (if comprehended it be) ; instead of informing the 
understanding through the eye, it at best only addresses the eye 
through the understanding. Difficult, — we only regret that it had 
not been impossible. 

4°. It is clumsy, operose, complex, and superfluous. Por, to re- 
present a notion denoted by a single angle, it is compelled to give 
the redundance of a whole triangle ; and three repugnant notions 
demand an apparatus of three several figures, and six vacant 
angles. In fact, the only manifestation to which this scheme of 
angles can pretend, is borrowed from the scheme of figures which 
it proposes to supersede. 

5°. It is wholly dependent upon the accidents of foreign aid. 
To let it work at all, it calls in to its assistance an indefinite plu- 
rality of figures, a Greek and Latin alphabet, combinations of let- 
ters straight and defiected, and an assortment of lines, thick and 
thin, plain and dotted. I have counted one diagram of the 
eighteen, and find that it is brought to bear through three varie- 
ties of line, four triangles, and eleven letters. 

It is needless to enumerate its other faults, its deficiences, ex- 
cesses, ambiguities, &c. ; transeat in pace. 

(c) The Author's Notation. — No. I. Lineae. 

The notation previously spoken of,« represents every various 
syllogism in all the accidents of its external form. But as the 
number of Moods in Syllogisms Analytic and Synthetic, Intensive 
and Extensive, Unfigured and Figured, (and of this in all the 
figures,) are the same ; and as a reasoning, essentially identical, 
may be carried through the same numerical mood, in every genus 
and species of syllogism : it seems, as we should wish it, that 
there must be possible also, a notation precisely manifesting the 
modal process, in all its essential diff"erences, but, at the same 
time, in its internal identity, abstract from every accidental variety 
of external form. The anticipation and wish are realised ; and 
realised with the utmost clearness and simplicity, in a notation 
which fulfils, and alone fulfils, these conditions. This notation 
I have long employed : and the two following are specimens. 

« See Tabular Scheme at the end of the present volume. — Ed. 



APPENDIX. 465 

Herein, four common lines are all the requisites : three (horizon- 
tal) to denote the terms ; one (two ? — perpendicular) or the want 
of it, at the commencement of comparison, to express the quality 
of affirmation or of negation ; whilst quantity is marked by the 
relative length of a terminal line within, and its indefinite excur- 
rence before, the limit of comparison. This notation can repre- 
sent equally total and ultra-total distribution, in simple Syllogism 
and in Sorites ; it shows, at a glance, the competence or incompe- 
tence of any conclusion ; and every one can easily evolve it. 



C 
M 
r " 



} 



c 
]\I 

r 



Of these : the former, with its converse, includes, Darii, Dabi- 
tis, Datisi, Disamis, Dimaris, &c. ; whilst the latter, with its con- 
verse, includes Celarent, Cesare, Celanes, Camestres, Cameles, 
&c. But of these, those which are represented by the same dia- 
gram are, though in different figures, formally, the same mood. 
For in this scheme, moods of the thirty-six each has its peculiar 
diagram ; whereas, in all the other geometrical schemes hitherto 
proposed, (whether by lines, angles, triangles, squares, parallelo- 
grams, or circles), the same (complex) diagram is necessarily 
employed to represent an indefinite plurality of moods. These 
schemes thus tend rather to complicate, than to explicate, — rather 
to darken, than to clear up. The principle of this notation may 
be realised in various forms." 



The problem, in general, is to manifest by the differences and 
relations of geometrical quantities, (lines or figures), the differences 
and relations of logical forms. The comparative excellence of any 
scheme in solution of this problem will be in proportion as it is, 
r. Easy; 2°, Simple; 3°, Compendious; 4°, All-sufficient; 5°, 
Consistent ; 6°, Manifest ; 7°, Precise ; 8°, Complete. 

In the scheme proposed by me, 

a Reprinted from Discussions, p. 657. tions denoted by the diagi-ams, see 
For a further explanation of the rela- above, vol. i. p. 189. — Ed. 

VOL. II. 2 G 



4^06 APPENDIX. 

1". I denote terms or notions by straight lines ; and, as a syllo- 
gism is constituted by three related notions, it will, of course, be 
represented by three related lines, 

2°. I indicate the correlation of notions by the order and par- 
allel coextension of lines. (The perpendicular order and horizon- 
tal extension, here adopted, is arbitrary.) 

3°. Lines, like notions, are only immediately related to those 
with which they stand in proximity. Hence, the intermediate 
line in our diagram, representing the middle term of a syllogism, 
is in direct relation with the lines, representing the extremes, 
whereas the latter are only in mutual correlation through it. 

4°. The relative quantity of notions is expressed by the com- 
parative length of the related lines. In so far as a line com- 
mences, (here on the left), before another, it is out of relation with 
it, — is indefinite and unknown. Where a line terminates under 
relation, (here towards the right), it ceases absolutely to be. A line, 
beginning and ending in relation, indicates a whole notion. A 
line, beginning before or ending after its correlative, indicates the 
part of a notion. 

5°. The kinds of correlation, Affirmation and Negation, are 
shown by the connection, or non-connection, of the lines, (here 
from the left). The connection, (here a perpendicular line), indi- 
cates the identity, or coinclusion, of the connected terms ; the 
absence of this denotes the opposite. The lines in positive or affirma- 
tive relation are supposed capable of being slid into each other. 

This geometric scheme seems to recommend itself by all the 
virtues of such a representation, and thus stands favourably con- 
trasted with any other. Por it is easy, — simjjle, — compendious, — 
all-sufficient, — consistent, — manifest, — precise, — complete. 

1°, Easy. — Linear diagrams are more easily and rapidly drawn 
than those of figure ; and the lines in this scheme require, in fact, 
no symbols at all to mark the terminal differences, far less the 
double letterings found necessary by Lambert. 

2°, Simple. — Lines denote the quantity and correlation of 
notions far more simply than do any geometric figures. In those 
there is nothing redundant ; all is significant. 

8", Compendious. — In this respect lines, as is evident, are far 
preferable to figures ; but Lambert's linear scheme requires more 
than double the space sufficient for that here proposed. 



APPENDIX. 467 

4°, All-sufficieut. — Any scheme by figures, and Lambert's 
scheme by lines, is, in itself, unintelligible ; and depends on the 
annexation of accidental symbols, to enable it to mark out the 
differences and relations of terms. Lambert, likewise, endeavours 
to supply this exigency by another means, — by the fortuitous quality 
(his dottings) of certain lines. In our scheme lines, simple lines, 
and lines alone, are sufficient. 

5°, Consistent. — Lambert's linear scheme is a mere jumble of 
inconsistencies. Compared with his, those by figures are, in this 
respect, far jjreferable. But the present linear scheme is at once 
thorougho-oins;, unambiguous, and consistent. 

6°, Manifest. — In this essential condition, all other geometrical 
illustrations are lamentably defective. In those by figure, each 
threefold diagram, typifying an indefinite plurality of moods, re- 
quires a painful consideration to extract out of it any pertinent 
elucidation ; this is, in fact, only brought to bear by the foreign 
aid of contingent symbols. Nor can these schemes properly re- 
present to the eye the relation of the toto-total identity of a plu- 
rality of terms ; the intention requires to be intimated by the ex- 
ternal accident of signs. Lambert's lines sink, in general, even 
below the figures, in this respect. But as lines are here applied, 
the sole pertinent inference leaj)s at once to sense and under- 
standing. 

7°, Precise. — Ambiguity, vagueness, vacillation, redundancy, and 
withal inadequacy, prevail in the other schemes. In those by 
figure, one diagram is sometimes illustrative of as many as a dozen 
moods, positive and negative ; and a single mood may fall to be 
represented by four diagrams, and perhaps in six several ways. 
Lambert's lines are even worse. In our scheme, on the contrary, 
every mood has a diagram applicable to itself, and to itself exclu- 
sively, whilst every possible variety of its import has a correspond- 
ing possible variety of linear difference. 

8°, Complete. — In this last and all-important condition, every 
scheme, hitherto proposed, is found to fail. A thoroughgoing, 
adequate, and pliant geometric method ought equally and at once 
to represent the logical moods in the Unfigured and Figured Syllo- 
gism, in the Syllogism Synthetic and Analytic, in Extension and 
Intension, — this, too, in aU their mutual convertibilities, and in all 
their individual varieties. This our scheme performs ; but exclu- 



4G8 APPENDIX. 

sively. So much, in general. Again, in particular : — Of the 
figures, circles and triangles are necessarily inept to represent the 
ultra-total inclusion or coexclusion of terms, — in a word, all the 
relations of jjroportion, except totality and indefinite partiality ; 
whilst quadrilateral figures are, if not wholly incompetent to this, 
operose and clumsy. Lambert's linear method is incompetent to 
it in negatives ; and such inability ought to have opened his eyes 
upon the defects of his whole plan, for this was a problem which 
he expressly proposed to accomi}lish. The present scheme, on the 
other hand, simply and easily joerforms this, in affirmation and 
negation, and with any minuteness of detail. 



Author's Scheme of Notation — Unfigured and Figured 
Syllogism — No. II. 

(1853.) The following Diagram affords a condensed view of 
my other scheme of Syllogistic Notation, fragments of which, in 
detail, will be found in Mr Thomson's Outline of the Laws of 
Thought, and in Mr Baynes' Essay on the New Analytic of 
Logical Forms. The paragraphs appended will supply the neces- 
sary explanations. 



APPENDIX. 



469 




Breadth 



»»»»» 



Order 



Ei ihcr or ]S!e i iJi er. 




1.) A Proposition, (hiaarr]ixa,intervallum,'Trp6Tacn^, literally 
X)rotensio, the stretching out of a line from point to point), is a 
mutual relation of two terms {ppoC] or extremes (aKpa). This is 
therefore well represented, — The two terms, by two letters, and 
their Eelation, by a line extended between them. 

2.) A Syllogism is a complexus of Three Terms in Three Pro- 
positions.— It is, therefore, adequately typified by a Triangle,— by 
a Figure of three lines or sides. 



470 APPENDIX. 

3.) As upwards and downwards is a procedure arbitrary in the 
diagram, the diagram indicates that we can, indifferently, either 
proceed from the Premises, (rationes), to the Conclusion {ratio- 
natuni), or from the Conclusion to the Premises ; the process 
being only in different points of view, either Synthetic or Ana- 
lytic. (An exclusive and one-sided view, be it remembered, has 
given an inadequate name to what are called Premises and Con- 
clusion.) 

4.) Eationally and historically, there is no ground for consti- 
tuting that Premise into Major which is enounced first, or that 
Premise into Minor which is enounced last. (See after, p. 697, 
&c.) The moods of what is called the Fourth Figure, and the In- 
direct moods of the First Figure, are thus identified. — In the 
diagram, accordingly, it is shown, that as right or left in the order 
of position is only accidental, so is first or last in the order of 
expression. 

5.) The diagram truly represents, by its various concentric 
triangles, the Unfigured Syllogism, as involving the Figured, and, 
of the latter, the First Figure as involving the two others. (In 
fact, the whole differences of Figure and Figures are accidental ; 
Moods alone are essential, and in any Figure and in none, these 
are always the same and the same in number.) 

6.) Depth and Breadth, Subject and Predicate, are denoted by 
the thick and thin ends of the same prepositional line. 

7.) Depth and Breadth are quantities always coexistent, always 
correlative, each being always in the inverse ratio of the other. — 
This is well shown in the connection and contrast of a line gradu- 
ally diminishing or increasing in thickness from end to end. 

8.) But though always coexistent, and consequently, always, 
to some amount, potentially inferring each other, still we cannot, 
without the intervention of an actual inference, at once jump 
from the one quantity to the other, — change, per saltum, Predicate 
into Subject and Subject into Predicate. We must proceed gra- 



APPENDIX. 471 

datim. We cannot arbitrarily commute the quantities, in passing 
from the Qusesitum to the Premises, or in our transition from the 
Premises to the Conclusion. When this is apparently done, (as in 
the Indirect moods of the First Figure and in all the moods of the 
Fourth), the jDrocedure is not only unnatural, but virtually complex 
and mediate ; the mediacy being concealed by the concealment of 
the mental inference tuhich really precedes. — Indicated by the 
line and broken line for the First Figure. 

9). In Syllogism, Figure and the varieties of Figure are deter- 
mined by the counter relations of Subject and Predicate subsisting 
between the syllogistic terms, — between the Middle and Extremes. 
— All adequately represented. 

10.) Figure and the differences of Figures aU depending upon 
the difference of the mutual contrast of Subject and Predicate 
between the syllogistic terms ; consequently, if this relation be 
abolished, — if these terms be made all Subjects, (or it may be all 
Predicates), the distinction of Figure will be abolished also. (We 
do not abolish, be it noted, the Syllogism, but we recall it to one 
simple form.) — And this is represented in the diagram. For as 
the opposition of Subject and Predicate, of Depth and Breadth, is 
shown in the opposition of the thick and thin ends of the same 
tapering line ; so where, (as in the outmost triangle), the preposi- 
tional lines are of uniform breadth, it is hereby shown, that all 
such opposition is sublated. 

11.) It is manifest, that, as we consider the Predicate or the 
Subject, the Breadth or the Depth, as princii^al, will the one pre- 
mise of the Syllogism or the other be Major or Minor ; the Major 
Premise in the one quantity being Minor Premise in the other. — 
Shown out in the diagram. 

12.) But as the First Figure is that alone in which there is such 
a difference of relation between the Syllogistic Terms, — between 
the Middle and Extremes ; so in it alone is such a distinction between 
the Syllogistic Propositions realised. — By the diagram this is made 
apparent to the eye. 



472 APPENDIX. 

13.) In the Unfigured Syllogism, and in the Second and Third 
Figures, there is no difference between the Major and Minor Terms, 
and, consequently, no distinction, (more than one arbitrary and 
accidental), of Major and Minor Propositions. — All conspicuously 
typified. 

14.) All Figured Syllogisms have a Double Conclusion ; but 

in the different figures in a different way. — This is well repre- 
sented. 

15.) The Double Conclusions, both equally direct, in the Second 
and Third Figures, are shown in the crossing of two counter and 
corresponding lines. — The logicians are at fault in allowing Indi- 
rect Conclusions in these two figures, — nor is Aristotle an excej)- 
tion. (See Pr. An., I., vii. § -i.) 

16.) The Direct and Indirect Conclusions in the First Figure 
are distinctly typified by a common and by a broken line ; the 
broken line is placed immediately under the other, and may thus 
indicate, that it represents only a reflex of, — a consequence through 
the other, (/car avaKkacriv, reflexim, ^;cr rejiexionem). The 
diagram, therefore, can show, that the Indirect moods of the First 
Fio;ure, as well as all the moods of the Fourth, ought to be re- 
duced to merely mediate inferences ; — that is, to conclusions 
from conclusions of the conjugations or premises of the First 
Figure. « 



[The following Table affords a view in detail of the Author's 
Scheme of Syllogistic Notation, and of the valid Syllogistic Moods, 
(in Figure), on his doctrine of a quantified Predicate. In each Figure, 
(three only being allowed), there are 12 Affirmative and 24 Nega- 
tive moods ; in all 36 moods. The Table exhibits in detail the 12 
Affirmative Moods of each Figure, and the 24 Negative Moods of 
the First Figure, with the appropriate notation. 

* rieprinted fi-oiu Discussions, p. 6^7-061. — Ed. 



APPENDIX. 473 

The letters C, V, each the third letter in its respective alphabet, 
denote the extremes ; the letter M denotes the middle term of the 
syllogism. Definite quantity, (allj any), is indicated by the sign 
(:) ; indefinite quantity, (some), by the sign (, or ,). The hori- 
zontal tapering line ( » ) indicates an affirmative relation 

between the subject and predicate of the proposition. Nega- 
tion is marked by a perpendicular line crossing the horizontal 
( ^ I )■ The negative syllogisms, in all the Figures, are exactly 
double the number of the affirmative ; for every affirmative 
affords a double negative, as each of its premises may be marked 
by a negative. In Extension, the broad end of the line denotes 
the subject, the pointed end the predicate. In Comprehension 
this is reversed ; the pointed end indicating the subject, the 
broad end the predicate. By the present scheme of notation, 
we are thus able to read a syllogism both in Extension and in 
Comprehension. The line beneath the three terms denotes the 
relation of the extremes of the conclusion. Predesignation of 
the conclusion is marked only when its terms obtain a different 
quantity from what they hold in the premises. Accordingly, 
Avhen not marked, the quantification of the premises is held re- 
peated in the conclusion. In the Second and Third Figures, — a 
line is inserted above as well as below the terms of the syllogism, 
to express the double conclusion in those figures. The symbol 
^-^y — ' shows that when the premises are converted, the syllogism 
remains in the same mood ; ^^^><:^ shows that the two moods 
between which it stands are convertible into each other by con- 
version of their premises. The middle term is said to be Balanced, 
when it is taken definitely in both premises. The extremes are 
balanced, when both are taken definitely ; unbalanced, when the 
one is definite, and the other is not. 

The Table here given exhibits the author's final arrangement 
of the Syllogistic Moods. The Moods are either A), Balanced, or 
B), Unbalanced,. In the former class both Terms and Propositions 
are Balanced, and it contains two moods, — i. ; ii. In the latter 
class there are two subdivisions. For either a), the Terms are 
Unbalanced, — iii. iv. ; or b), both the Terms and Propositions are 
Unbalanced, — v. vi. ; vii. viii. ; ix. x. ; xi. xii. 

It should be observed that the arrangement of the order of 
Moods given in the present Table, differs from that of the earlier 



474; APPENDIX. 

scheme printed above, p. 287 et seq. The following is the corre- 
spondence in the order of moods : — 



Present and 
Final Table. 




Earlier 
Table. 


I. 


corresponds to 


I. 


II. 


... ... 


II. 


III. 


... ... 


XI. 


IV. 




XII. 


V. 


... ... 


VII. 


VI. 




VIII 


VII. 




III. 


VIII. 


... ... 


IV. 


IX. 


... ... 


V. 


X. 


... ... 


VI. 


XI. 


... ... 


IX. 


XII. 





X. 



The order of the earlier table is that given by Mr Baynes, in the 
scheme of notation printed at p. 76 of his Essay on the New Ana- 
lytic. The order of the present table corresponds with that given 
by Dr Thomson in his Laivs of Thought, p. 244, 3d edition, 1853. 
—Ed.] 



APPENDIX. 



4«.')-(j 



SCHEME OF NOTATION— FIG U If ED SYLLOGISM. 
TABLE OF SYLLOGISTIC MOODS. 



Fig. I 

M: 



A. AFFIRMATIVE MOODS. 

Fig. II. 



Fig. III. 



; : M: iF C: : M : :r C:- •• M : -T . f 

I. i 



B. NEGATIVE MOODS. 

Fig. I. 
a C:-+— ■ M : :r 



C, : M : — ..r C, : M : — ,r C- : M : ^.r 



C- 



: M, 



■•r C'- 



M, 



:r C 



M 



1 b c= 

a C. 4— 

b C. 

j a C> ^ 



b C- 



M 



M 






M 



. M 



-.r C: 



,M: ,r C> 



, M 



-.r 



/ V. C. : M, ^.r C,^ : M , ^,r c.- — ■- M , — ,r 



B 



j a C: H— . M •■ ^ .r 

{ b C: ^ ' M : -|- ,r 

a C. 4— = M , ,r 

:M, 



b C' 
j a C 



,M 



C. , M : .,r C, , M : — ,r C, , M : ,T ''■ | ^ C, , M 



vii. C 

viii. C- 

ix. C:- 
»- 

X. C:- 
xi. C:- 



: :M: ..r C: :M: ,r C-" - ^ '■ 'T vii. \ 



a C: 



: M 



M, 



, M: 



:M, 



.:r 


c, 


:r 


C:- 




>' 


:r 


C:- 


,r 


C:- 



: M 



:M, 



,M: 



M, 



:r 


c 


.r 


c 


T 


c 


r 


c' 



: M 



:M, 



, M: 



:U, 



-:r 

■T 



[ b C: 

a G, -\— 
b C. ■ 

( a C:-f— _ 

( b C= 

a C:H--_ 
b C= 

I a C:-]— 



M 



M 



,r 
.r 
,r 
,r 
,r 
:r 
:r 

.r 

M. j--:r 

-.T 



M 



M 



M, 



.¥ 



t: 



{ b C: ■ :M, 



C, , M : :r C, , M : 'r C» » M : ..r 



a C,-t— . M : 



b C, M : 



,r 
,r 
■.r 
•r 



A. i. and ii. are Balanrrrl. B. The other moods are Unbalanced. Of these, iii. and iv. are unbalanced in terms only, not in propo.sitions ; the rest in both. 



INDEX. 



AbstrajCT or General Logic, see Logic. 

Abstraction or Generalisation, what, L 
123 ; 1-17-8 ; its synonyms, ib. 

Academical Disputation, ii. 224r-5. 

Accidents, or Extrinsic Denominations, 
what, i. 217. 

Acquisition of Knowledge, doctrine of, 
see Logic. 

Affections or Passions, as a source of 
error, see Error, Causes of. 

Afranius, quoted on the nature of exi)e- 
rience, ii. 1.56. 

Agi-icola, Rodolphus, i. 2S2. 

Albertus ^Magnus, referred to on genus 
of Logic, i. 9 ; quoted on province of 
Logic, 27 ; quoted on quantification of 
predicate, ii. 309-10. 

Aldrich, Dean, his Comjiendiiim, i. 29 ; 
his abusive employment of the terms 
hypothetical and conditional, 236 ; his 
abuse of the phrase in-opositio erposiia, 
263 : 350. 

Alexander of Aphrodisias, the oldest com- 
mentator on Aristotle, i. 5 ; referred 
to as to his use of the term \oyiK^, 
ib. ; has the distinction of Abstract 
or General and Applied or Special 
Logic, 53 ; his illustration of the dis- 
tinction, 53-4, see Logic ; 2S2 ; 2S3 ; 
on principle of name of major and 
minor terms, 294 ; 306 ; 33S ; referred to 
on quantity of hypothetical syllogisms, 
348 : 391 ;" 414 ; ' ii. 3 ; -256 ; quoted on 
quantification of predicate, 303 ; his 
ground of the discrimination of major 
and minor terms in the second and third 
Figures, 40S-9 ; certain early Greek 
logicians mentioned by, who recognised 
no major or minor term in the second 
and third Figm-es, 409-10 ; (and Her 
minus), quoted on figure of syllogism, 
415-20. 
Alexander de Ales, or Alensis, held the 
law of Contradiction to be the primaiy 
principle of knowledge, i. 92 ; but, in 
fact, identified it with that of Ex- 
cluded Middle, ib. 
Alstedius, on the principle of Contradic- 



tion, i. 88 : partially anticipated Lana- 
bert in the use of parallel lines as logi- 
cal notation, 256. 
Alvarez, i. 456. 

Ammonius Hermije, referred to on genus 
of Logic, i. 9 ; 54 ; on the principle of 
Contradiction, 88 ; 191 : 226 ; 245 ; 
279 ; 33S ; 391 ; referred to on the 
\6yos Bipi^wv, or reajier, 463 ; 466 ; ii. 3 ; 
referred to on Division and its various 
kinds, 22 ; referred to on Greek article, 
280 ; quoted on q\iantification of pre- 
dicate, 299, 303-6; quot«d on Hypo- 
thetical (Conjunctive) and Disjunctive 
Syllogisms, 388-92 ; (and Philoponus), 
their ground of the discrimination of 
major and minor terms in the second 
and third Figures, 403. 

Analogy, what, ii. 165-6 ; 170-71 ; founded 
on the principle of Philosophical Pre- 
sumption, 166 ; its agreement vith and 
distinction from Induction. 166-7 ; has 
two essential conditions, 171-2 ; sum- 
mary of the doctrine of, 172 : Induction 
and "Analogy compared together, 172-3 ; 
these do no"t afford absolute certainty, 
173-4 ; authors referred to on, 174. 

Analysis, see Method. 

Analytic, name employed by Aristotle to 
denote a particular part of Logic, i. 8. 

Anaximenes, of Lampsacus, the treatise 
PJietoi-ic to Ale.rander attributed to, i. 
390. 

AnciUon, Frederic, referred to, i. 44. 

Andreas, Antouius, the first to explicate 
the law of Identity as a co-ordinate 
principle, i. 91. 

Anscftauunp, expresses what is common to 
Perception and Imagination, as opposed 
to Conception, viz.", the indiriduali^ 
andimmediacv of their objects, i. 126-7 ; 
183 : can be" translated into English 
only by Infu ition, but ambiguously, 127. 

Ani/toloffia Grceca, i. 393. 

'AirapiBfiricris, its character and meaning, 
ii. 23. 

Apodeictic, employed by Aristotle to de- 
note a particular part of Logic, i. 8. 



478 



INDEX. 



Apophantic^ nee Jvidg^ments, Doctrine of. 
' h-K6(pav(ns, its use by Aristotle, i. 22(j. 
Applied Loijic, the expression, Low em- 
ployed by Kant, i. tiO ; can only with 
propriety be used to denote Special or 
Concrete Logic, and is improperly em- 
ployed as a designation of Modified Lo- 
gic, (il. 
Apuleius, i. 414. 

Aquinas, St Thomas, i. f<S ; referred to 
on classification of the Categories, 200 ; 
his definition of truth quoted, ii. G3. 
Arabian Schoolmen, viewed Logic as a 

science, i. 9. 
'Apx^ TTjs Yi/wtrews, distinguished by Aris- 
totle from the apxv'''V^ yeveaewSj i. 93. 
Argument, properly denotes the middle 
notion in a reasoning, i. 278 ; how de- 
fined by the Latin Rhetoricians, 278-9 ; 
often employed as coextensive with 
argumentation, 279. 
Aristotelic questions, An sit, &c., referred 

to, ii. 158. 
Aristotelians, ancient Greek, denied Logic 
to be either science or art, i. 9 ; their 
views on the object-matter of Logic, 
27. 
Ai-istotelians, modern, many of them main- 
tained Logic to be an art, i. 9. 
Ai'istotle, quoted, i. 5 ; his employment 
of the term Dialect ie, 8 ; did not "define 
liOgic, 9 ; his relation to views of the 
nature and domain of Logic, 26-7 ; by 
far the greater number of his logical 
writings lost, 26 ; none of his treatises 
affords a view of Logic from a central 
point, ih. ; gave no general definition of 
Logic, ih. ; said that medicine begins 
where the philosoph}' of nature leaves 
off, 36 ; emphatically enounced the law 
of Contradiction, 87 ; explicitly enoun- 
ced the principle of Excluded Middle, 
90-1 ; recognised the law of Reason 
and Consequent, 93 ; distinguished it 
from the principle of Production, ih. ; 
said that the doctrine of Syllogisms 
deals not with the external expression, 
but with the internal reasoniiig of the 
mind itself, 115; see also 388; used 
voy)fiara in a sense equivalent to con- 
cepts, 120 ; his first anti-prEedicamental 
rule quoted, 144 ; this rule translated 
by the Nota notce e.<<t nota rei ipsius, ih. ; 
his Categories, what, 196, see Categories; 
n(jticed the difference of Potential and 
Actual Wholes, 207 ; referred to on in- 
clusion of Copula in prajdicate, 228 ; 
called subject and predicate, the terms 
or extremes of a proposition, ih. ; called 
a proposition an Interval, Sidarrifia, 
229 ; allowed only four kinds of modal- 
ity, 257 ; described Sub-contrary oppo- 
sition as merely in language, 261, see also 
ii. 281 ; his conversion eV fj-epet, 264 ; 
noticed Couversion^jfic Coiitrapositionem, 
under the name of the inverse consecution 
from contradictions, ih. ; his employment 



of the tei-m (KOecrts, e.vposition, 263 ; his 
expression for Simple Conversion, ih. ; 
his A nali/lics are SjTithetic, 277 ; 
see alio ii. 401 ; his definition of the 
terms of a Syllogism, i. 299 ; his defini- 
tion of the middle, as middle by posi- 
tion, not applicable to the mode in 
which subsequent logicians enounce the 
syllogism, ih. ; but"" applicable to the 
reasoning in comprehension, 299-300 ; 
did not, however, necessarily contem- 
plate the reasoning in comprehension, 
300 ; enounced the canons both of Ex- 
tensive and Comprehensive reasoning, 
303 ; 342 ; his law,— that the whole is 
necessarily conceived as prior to the 
part, —criticised by the Author, 357-9; 
only once vaguely alluded to the 
process of what was afterwards called 
Sorites, 375 ; his rule translated Pra;- 
dicat/im pra-dicati, &c., contains the 
principle of Sorites, ih. ; did not dis- 
criminate the vulgar Enthymeme as 
a distinct species of reasoning, 388- 
9 ; his Enthymeme a syllogism from 
signs and likelihoods, 389 ; Rhetoric 
to Ale.rander attributed to, 390 ; the 
term (Tx^)ixa, Figure, due to, 400; distin- 
guished the first three figures, ih. ; 413; 
415 ; 454 ; 466; ii., 6 ; his distinction of 
the two modes of scientific procedure 
as from, and to, principles, 8; 12; his 
argument for slavery a petitio prin- 
cipii, 53 ; referred to and quoted on 
knowledge and belief, 70-1 ; his pre- 
cept regarding the subjugation of self- 
love, 102 ; 137 ; 206 ; quoted on ability 
to teach as a mark of knowledge, 
210; first systematically developed Logic 
proper, 231 ; referred "to on postulates 
of Logic, 552-3; quoted against quantifi- 
cation of predicate, 298-303 ; the true 
meaning of his e.fse in toto, and did 
de omni, 301-2 ; his doctrine of prede- 
signation, 302-3 ; syllogisms in his writ- 
ings which are valiil only thi-ough quan- 
tification of the pi-edicate, 302 ; 346 • 
his doctrine of Induction and Example, 
358-62 ; ignored the Disjunctive and 
Hypothetical syllogisms of the logicians, 
376 ; quoted and referred to on Hypo- 
thetical syllogism, 387-8 ; his syllogisms 
ex It >/pot/iesi, —whether correspon<lent to 
the ordinary hypothetical syllogism, — 
authors referred to on, 388 ; his doctrine 
of the discrimination of major and minor 
terms in the second and third Figure, 
407 ; ipioted on Figure and Terms of syl- 
logisms, 413-14. 

Arnauld, along with Nicole, author or 
the Port-Ro3'al Logic (L'Art de Penser), 
i. 70 ; referred to as holding that men 
are naturally envious, ii. 105 ; quoted 
on figure of Syllogism, 426-7. 

Arnoldus de Tungeri, his doctrine of In- 
duction, ii. 367. 

Arrian, referred to on the argmnent called 
x6yos KvptevcDV, i. 464. 



I 
I 



INDEX. 



479 



Arseniiis, i. 4GS. 

Ai-t,' ancient and modern, diverse charac- 
ters of, ii. 131-2. 

Association, laws of, what, ii. r22-3. 

Association or Suggestion, as a source of 
Error, see Error, causes of. 

Assumption, name for Minor Premise, i. 
2S5 ; but not a suitable term, ib. 

Attention, the act of, how constituted, i. 
123 ; Prescision, Abstraction, and At- 
tention correlative terms, 123. 

Augustin, St, his answer to the question 
what time is, i. 167. 

Augustin, Pseudo, referred to on inapplica- 
bility of the categories to Deity, i. 198. 

Augustinvis Niphus Suessanus, i. 88. 

Aulus Gellius, i. 464 ; 466. 

Authenticitj', criticism of, see Testimony. 

Averroes, quoted on use of the Ai'abic 
article in quantification, ii. 2S0 ; quoted 
on quantification of predicate, 309 ; 
quoted on figure of syllogism, 425-6 ; 
quoted on fourth Figure, 454. 

Avicenna, ii. 167 ; 171. 

Axioma, used by Stoics and Ramists as a 
synonym iov jiropoyition, i. 266. 

A^ioofia rris a,yTL(pd(recjt>s,^^Tiarao applied by 
Ammonius and I'hiloponus to principle 
of Contradiction, i. 88, see Contradic- 
tion, principle of. 

Axioms, what, i. 266. 

Bachmann, referred to on the analogy 
between Logic and Mathematics, i. 44 ; 
94-5 ; 124 ; 210 ; 230 ; 254 ; 259 ; 282 ; 
306 ; 309 ; 311 ; 334 ; 342 ; 404 ; quoted, 
with brief or-iginal interpolations, on 
the fig-ures and moods of Sjdlogism, 
405-22 ; his reduction of Baroco, 440 ; 
quoted on character of ancient Greek 
Sophisms, 452-4 ; ii. 81 ; quoted on the 
prejudice of learned authority, 87-8 ; 
114-18 ; 134 ; 151 ; 174. 

Bacon, Lord, wholly misconceived the 
character of Logic in cei tain respects, 
i. 29 ; at fault in his criticism of Aris- 
totle's doctrine of Induction, 325; called 
empirical generalisations axioms, ii. 47; 
his classification of the sources of error, 
80 ; quoted on reading, 223 ; the aim of 
his Organon, 231. 

Balfour, or Balforeus, referred to on a 
spurious pas.sage in A.v\&iot\e's Rhetoric, 
i. 8 ; quoted on illustration by the 
Aphrodisian of Abstract and Applied or 
Special Logic, 54 ; on Abstract and Ap- 
plied or Special Logic, 62. 

Ba0os, its meaning in relation to concepts, 
i. 141. 

Baumgarten, A. G., the Leibnitian, the 
first to iise the term 2)>'i'ici2>i>i'it- exdusi 
medii, i. 91 ; called the principle of 
Identity, jmncipium positionis sive 
■identitatis, 92 ; attempted to demon- 
strate the law of SufBcient Eeason by 
that of Contradiction, 95 ; 1 42 ; quoted 
on Canons of Syllogism, ii. 324-5. 



Baynes, Thomas Spencer, his Exsai/ on the 
Neio A nalylie of Logical Forms referred 
to, i. 42 ; his translation of the Port 
Royal Logic noticed, 70; 162 ; his Essay 
referred to, ii. 315. 

Begriff, the tenn in German philosophy 
for the symbolical notions of the under- 
standing, i. 1 83. 

Belief, see Truth and Error, doctrine of. 

Ben Gerson, or Gersonides, Levi, quoted 
on quantification of predicate, ii. .310-1 1. 

Beneke, i. 95 ; his doctrine of syllogism, 
ii. 439-42. 

Bertius, i. 279 ; 375. 

Beza, i. 3.93. 

Biel, Gabriel, his use of conceptus, i. 42. 

Biunde, ii. 63. 

Blemmidas, Nicephorus, i. 119 ; referred 
to on origin of distinction of proposi- 
tions secundi and tertii adjacentis, 228 ; 
quoted on import of the term ffvWo- 
■yifffjiSs, 279, 384 ; his Epitome for many 
contiu'ies the text-book of Logic in the 
schools of the Greek Church, 432 ; 
mentioned as the inventor of the Greek 
mnemonic verses for mood and figure 
of syllogism, 432; but, according to 
later view, these verses only a transla- 
tion of the Latin, 432: ii. 256; quoted 
on Contingent Conversion, 265. 

Boethius, referred to on the application of 
the term logic, i. 5, 142, 156 ; his divi- 
sion of Conversion, 264 ; the first to 
give the name C'oiiversio per accidens, 
ib. ; nature of this process as employed 
by, ih., 282; quoted for wse oi sumptum 
OAvl asmmplio, 285; referred to on use 
of terms poucus and tollens, in connec- 
tion with hypothetical syllogism, 338, 
414 ; ii. 14 ; quoted on the influence of 
passion on the mind, 94 ; 256 ; quoted 
on quantification of predicate, 306-9. 

Bolzano, i. 33S ; 344; ii. 174. 

Bojde, Hon. Robert, referred to for dis- 
tinction of reason iJi ahstracto, and rea- 
son in coiicreto, i. 60. 

Brandis, Ch. A., referred to on the title 
Organoti for the logical treatises of 
Aristotle, i. 34 ; 191. 

Braniss, Ch. J., i. 262 ; 448. 

Breadth and Depth, names for the exten- 
sion and comprehension of concepts, i. 
141 et alibi. 

Buchanan, George, i. 393. 

Buffier, i. 159 ; ii. 14 ; quoted on canons 
of syllogism, 337-8. 

Burgersdyk, or Burgersdicius, referred to 
on genus of Logic, i. 9 ; his Institvtioiies 
Logicce noticed and recommended, 71 ; 
ii. 225 ; referred to on Whole and Part, 
202 ; quoted on Potential and Actual 
Whole, 206-7 ; 415. 
Buridanus, his sophism of the Ass re- 
ferred to the head of Sophisma Hetero- 
zeteseos, i. 466. 
Burleigh, Lord, his practice in reading, 
ii. 216-17. 



480 



INDEX. 



Butler, Samuel, quoted as to tte princi- 
pal utility of Rhetoric, i. 48. 

Cajetan, Cardinal, quoted for his use of 
the terms intensive and extensive in rela- 
tion to notions, i. 141. 

Calker, i. 141. 

Camerarius, Gul., referred to on g'enus of 
Logic, i. 9 ; referred to for scholastic 
theories on the object-matter of Logic, 
27-8. 

Campbell, Principal, quoted on indis- 
tinctness of terms, i. 175-6. 

Capella, Martianus, quoted on figure of 
syllogism, ii. 424-5. 

Caramuel, see Lobkowitz. 

Carleton, Thomas Compton, referred to 
on tho metaphysical character of the 
Categories of Aristotle, i. 199. 

Caro, quoted, ii. 104-(j ; 114 ; 144. 

Cartesians, majority of, maintained Logic 
to be an art, i. 9. 

Cassiodorus, i. 392 ; ii. 424. 

Categorical Proposition, better styled 
Absolute or Perfect, i. 233, see Judg- 
ments, doctrine of. 

Categorical, the term, as used by Aris- 
totle, equivalent to affirmative, i. 234 ; 
its application by Theophrastus and 
Eudemus, in opposition to conclitiottal, 
234-5 ; this difference of signification 
not hitherto observed, 235. 

Categories or Predicaments of Aristotle, 
what, i. 19(3 ; original meaning of the 
term Category, 197 ; its employment by 
Aristotle, ih. ; by Plotinus, ih. ; by 
Kant, 197-8 ; the Categories of Aris- 
totle metaphysical, 199 ; criticised as a 
classification of being, 199-200; objects 
not included under, 198 ; diversity of 
opinion among logicians regarding 
their number, 200 ; various authors 
referred to i-egarding, 200-1. 

Certainty, see Truth and Error, Doctiine of. 

Chauvin, i. 265. 

Cicero, referred to on the use of Logica, 
i. 6 ; probably borrowed his use of that 
term from the Stoics, ih. ; quoted on 
the province of Logic, 37 ; enounced 
the principle of Excluded Middle, 91 ; 
recognised the principle of Reason and 
Con.sequent, 93 ; his definition of argu- 
mentum quoted, 279 ; applied the term 
Sorites to an argument like the modern 
Sorites, but which coxdd also be a 
Chrifsippean, 376 ; called the sophism 
Sorites Acervalis, ib. ; his employment 
of the term Hitthi/meme, 390 ; his state- 
ment of the /yHara liatio, 462; 465-6; 
ii. 103; 206-7. 

Circulus in demonstrando, see Probation. 

Classes, names for the different steps in 
the series of, in physical science, i. 201. 

Clearness and Obscurity, Distinctness and 
Indistinctness of Concepts, see Con- 
cepts, Quality of. 

Clement of Alexandria, quoted on teach- 



ing as a mean of self-improvement in 
knowledge, ii. 210. 

Clerc, see Le Clerc. 

Cogitatio (Thovght), its use by Descartes, 
i. 12 ; see Thought. 

Cognitive Faculties, Weakness and Dis- 
proportioned Strength of, as a source 
of error, see Error, Causes of. 

Coke, Zachary, his use of the term con- 
cept, i. 42. 

College of Alcala, the, see Cursus Complu- 
tensis. 

Communication of Knowledge, Doctrino 
of, see Logic. 

Comparison, Faculty of, its products 
threefold, — Concepts, Judgments, and 
Reasonings, i. 117 ; its offices, 122-3. 

Comprehension and Extension of Con- 
cepts, see Concepts, Quantity of, cuid 
Reasonings. 

Concept, should be used to denote the ob- 
ject conceived, i. 41-2 ; its derivation, 
42 ; many words in English formed on 
the same analogy as precept, digest, &.C. 
ib. ; was in common use in the sense 
proposed among the older English 
philosophical writers, ib. ; and among 
the old Fi-ench philosophers, ib. ; now 
employed in French in translating the 
German Begriff, ib., see also Conceptus; 
what, 76 ; its synonyms, 76-7 ; see Con- 
cepts, Doctrine of. 

Conceptio, its meaning, i. 120. 

Conception, employment of the term by 
Stewart to denote the simple represen- 
tation of an object presented in Percep- 
tion, i. 40 ; vacillation in its use by 
Reid, ib. ; sense in which employed by 
the author, ib. ; its derivation, 41 ; 
means both the act of conceiving and 
the object conceived, ib. ; should be 
used to denote exclusively the act of 
conceiving, and concept applied to the 
object conceived, 41-2 ; Reid quoted 
on, 109-12 ; his mistakes regarding, 
112-13 ; usually called by the logicians 
Simple Apprehension, 119. 

Concepts, Doctrine of, i. 116-24 ; of Con- 
cepts or Notions, order of discussion, — 
A. In general, what they are, and how 
produced, 118 et seq., 130 et seo. ; doc- 
trine of concepts omitted by Whately 
in his Elements, 118 ; a. Meaning of the 
terms Concept or Notion, 119-20 ; their 
synonyms, 119 ; Concept denotes the re- 
sult of the act of Conception, that is, 
of comprehending or grasping up into 
unity the various qualities by which an 
object is characterised, 120 ; Notion 
denotes either the act of apprehending 
the notes or marks of an object, or the 
result of that act, ib. ; employment of 
the terms animo vel mente concipere, and 
aninii conceptus, ib. ; of concipere, con- 
ceptus and concej)tio, without adjunct, ib. ; 
the term Notion how employed by the 
author, 121 ; b. Nature of the thing ex- 



INDEX. 



481 



pressed, 121 et seq.; a concept eqiiivalent 
to the mediate and relative knowledge we 
have of an object, as comprising qualities 
or characters common to it with other 
objects, 122 ; nature and production of 
concepts illustrated by reference to the 
history of our knowledge, 122 et seq. ; 
the results of comparison and abstrac- 
tion or attention, as operating on ob- 
jects originally presented in confused 
and imf)erfect perceptions, and reducing 
multitude to unity, 122-4 ; the reduc- 
tion of multitude to unity involved in 
conception explained and illustrated, 
124 et seq. ; thought one and the same, 
while its contents are identical, 124 ; 
objects are to us the same when we are 
unable to distinguish their cognitions, 
whether as wholes, or in their partial 
characters, 124-5; concepts or notions 
are constituted by the points of similar- 
ity discovered in objects, and identified 
in the unity of consciousness, 125 ; 
concepts may themselves become the 
objects of comparison and abstraction, 
12b" ; concepts or notions superfluously 
styled, (leaeral, ih.; general characters of 
concepts, 127 el seq., Vii: et seq. ; a. A 
concept affords only an inadequate 
knowledge of the thing thought under 
it, 127 et seq. ; b. Affords no absolute 
object of knowledge, but can be realised 
only by being applied as a term of rela- 
tion to one or more of the objects 
which agree in the point or points of 
resemblance which it expresses, 128 ; 
this doctrine explains the whole mystery 
of generalisation and general terms, ib. ; 
the generality of a concept is potential, 
not actual, 129-35 ; concepts are not, 
on that account, mere words, 136 ; c. 
Their dependence on language, 137 et 
seq. ; language necessary to the perfec- 
tion of concepts, 139 ; B. Of concepts 
or notions in special, 140 et seq. ; quantity 
of concepts, 141 et seq.; what is meant 
by saying that a concept is a quantity, 
143 ; this quantity of two opposite kinds, 
— Intensive or Comprehensive and Ex- 
tensive, 143-5(1, see Concepts, Quantity 
of; quality of Concepts, 157-86, ^eg Con- 
cepts, Quality of ; Reciprocal Relations 
of, 187 et seq., see Concepts, Reciprocal 
Relations of. 
Concepts, Quantity of, or Comprehension 
and Extension of Concepts, what, i. 
141-3, 146 ; how respectively desig- 
nated, 141; these quantities opposed 
to each other, 146 ; law regulating 
the mutual relations of, il>. ; this il- 
lustrated, 147 ; processes by which 
amplified and resolved, — Determination 
or Concretion, Abstraction or General- 
isation, Definition, and Division, 143-7; 
opposed in an inverse ratio, 14S-9 ; De- 
finition and Division the processes by 
which the Comprehension and Extension 
of concepts are respectively resolved. 



149-51 ; diagram representing, with re- 
lative illustration, 152-6. 
Concepts, Quality of, i. 157 et seq. ; this 
determined by their relation to their 
subject, 157 ; consists in their logical 
perfection or imperfection, 157, 158 ; 
this of two degrees, — Clearness and 
Distinctness, and Obscurity and In- 
distinctness, 158 ; these degrees distin- 
guished, 158-9; original application of 
the expressions clearness, obscurity, &c., 

159 ; illustrated by reference to vision 
and representation, 159-60 ; 163-5 ; 
clearness and obscurity as in concepts, 

160 et seq.; the absolutely clear and the 
absolutely obscure, 161 ; distinctness 
and indistinctness of, l62 ; historical 
notices of this distinction, 162 et seq. ; 
due to Leibnitz, 162 ; notice of Locke 
in connection with it, ib. ; difference 
between a clear and distinct knowledge 
illustrated, 163 et seq. ; the judicial de- 
termination of life and death sujiposes 
the difference between a clear and dis- 
tinct knowledge, 164 ; further illustra- 
tion from the human countenance, 164- 
5 ; special conditions of the distinctness 
of a concept, and of its degrees, 165-7 ; 
the distinction between clear and dis- 
tinct knowledge illustrated by examples, 
167 ; how the distinctness of a concept 
is affected by the two quantities of a 
concept, 168 et seq. ; distinctness is in- 
ternal and external, 168-9 ; relations of 
Definition and Division to internal and 
external distinctness, 169 ; simple no- 
tions admit of an extensive, individual 
notions of an intensive, distinctness, 
169 ; the highest point of the distinct- 
ness of a concept, 169-70 ; imperfection 
to which concepts are liable, in respect 
of the thought of which they are the 
expression, 171-2 ; this imperfection 
illustrated, 172 et seq. ; noticed by 
British philosophers, 174 ; Stewart 
quoted on the subject, 17^-7 ; Locke 
anticipated Hume in remarking the 
employment of terms without distinct 
meaning, 177 ; Locke quoted on this 
point, 177-9 ; the distinction of Intuitive 
and Symbolical knowledge first taken 
by Leibnitz, 179 ; this distinction su- 
perseded the controversy of Nominalism 
and Conceptualism in German}', 179-83 ; 
discussed by him in De Cognitione, Veri- 
late, et Ideis, 180 ; the passage quoted, 
181-2 ; the distinction appreciated by 
the disciples of Leibnitz, 183 ; Wolf 
quoted on, 184-6. 

Concepts, Reciprocal Relations of, i. 187- 
224 ; relation proper of, what, 187 ; can 
be compared together with reference 
only either, 1°, To their Extension, or, 2°, 
To their Comprehension, i6. ; considered 
A. As dependent on extension, 187-212 ; 
as dependent on extension, concepts 
stand to each other in the five mutual 
relations of Exclusion, Coextension, 



482 



INDEX. 



Subordination, Co-ordination, and In- 
tersection, 1S7-S ; examples of the five 
mutual relations of concepts, 188 ; dia- 
grams illustrative of, 189 ; of these 
relations, sub-ordination and co-ordina- 
tion of principal importance, ISO ; sub- 
ordination considered, 190-209; terms 
expressive of the different modes of the 
relation of stibordination, 190 ei seq. ; 
Superior, Inferior, Broader, Narrower 
Notions, 190; Universal, Particular, 
190-1; General Notion, Genus, Special 
Notion, Species, 191-2, «'(?e Genus and Spe- 
cies ; Co-ordination, what, 209; the two 
general laws by which subordination and 
co-ordination umk'r extension are regu- 
lated, viz., of Homogeneity and Hetero- 
geneity, 209-10 ; their import, 210 ; law 
of Heterogeneity, true only in theory, 
ih. ; additional law of Logical Affinity 
promulgated by Kant, but to be rejected, 
211 ; B. As dependent on compre- 
hension, but not in the relations of 
involution and co-ordination, 212-24 ; 
notions, in relation to each other, are 
Identical and Different, 212 ; identical, 
divided into absolutely and relatively 
identical, 212 ; alisolutely identical 
notions impossible, 212-13; relatively 
identical called also Similar and Re- 
ciprocating or Convertible, ih. ; notions 
are Congruent or Agreeing, and Con- 
flictive, 213-14 ; Congruent and Identi- 
cal notions, and Diverse and Conflictive 
distinguished, 214, see Concepts, Oppo- 
sition of ; Intrinsic and Extrinsic, 21 (i- 
17 ; Involution and Co-ordination in 
comprehension, 217, 220 ; these rela- 
tions of notions neglected by logicians, 
and hence also neglected reasoning in 
comprehension, 217 el seq. ; the rela- 
tion of the containing and the contained 
in comprehension properly called in- 
volution, 220 ; this illustrated, 220-21 ; 
the involving notion the more complex, 
the involved the more simple, 222 ; co- 
ordination in comprehension, 223-24 ; 
notions coordinated in comprehension 
called Disparate, in extension Disjunct 
or Discrete, 224. 

Concej^ts, Opposition of, arises un der Com- 
prehension, i. 213; constituted by con- 
tiiction, or the imiiossibility of being 
connected in thought, ih. ; twofold, 1*^, 
Immediate or Contradictory ; 2°, Medi- 
ate or Contrai-y, 213-14; these distin- 
guished and illustrated, 214-